{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T19:26:05Z","timestamp":1758396365379},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2007,8,8]],"date-time":"2007-08-08T00:00:00Z","timestamp":1186531200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2008,12]]},"DOI":"10.1007\/s10208-007-9002-0","type":"journal-article","created":{"date-parts":[[2007,8,7]],"date-time":"2007-08-07T16:20:15Z","timestamp":1186503615000},"page":"703-736","source":"Crossref","is-referenced-by-count":7,"title":["Coefficient Quantization in Banach Spaces"],"prefix":"10.1007","volume":"8","author":[{"given":"S. J.","family":"Dilworth","sequence":"first","affiliation":[]},{"given":"E.","family":"Odell","sequence":"additional","affiliation":[]},{"given":"T.","family":"Schlumprecht","sequence":"additional","affiliation":[]},{"given":"A.","family":"Zs\u00e1k","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,8,8]]},"reference":[{"key":"9002_CR1","doi-asserted-by":"crossref","unstructured":"S. A. Argyros, G. Godefroy, and H. P. Rosenthal, Descriptive set theory and Banach spaces, in Handbook on the Geometry of Banach Spaces, Vol.\u00a02 (W.\u00a0B.\u00a0Johnson and J. Lindenstrauss, eds.), pp.\u00a01007\u20131069, 497\u2013532, North-Holland, Amsterdam, 2003.","DOI":"10.1016\/S1874-5849(03)80030-X"},{"key":"9002_CR2","doi-asserted-by":"crossref","first-page":"1990","DOI":"10.1109\/TIT.2006.872849","volume":"52","author":"J. J. Benedetto","year":"2006","unstructured":"J. J. Benedetto, A. M. Powell, and \u00d6. Yilmaz, Sigma\u2013Delta (\u03a3\u2013\u0394) quantization and finite frames, IEEE Trans. Inform. Theory 52 (2006), 1990\u20132005.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"9002_CR3","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.acha.2005.04.003","volume":"20","author":"J. J. Benedetto","year":"2006","unstructured":"J. J. Benedetto, A. M. Powell, and \u00d6. Yilmaz, Second order Sigma\u2013Delta (\u03a3\u2013\u0394) quantization of finite frame extensions, Appl. Comput. Harmon. Anal. 20 (2006), 126\u2013148.","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9002_CR4","doi-asserted-by":"crossref","first-page":"151","DOI":"10.4064\/sm-17-2-151-164","volume":"17","author":"C. Bessaga","year":"1958","unstructured":"C. Bessaga and A. Pe\u0142czy\u0144ski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151\u2013164.","journal-title":"Studia Math."},{"key":"9002_CR5","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BFb0078132","volume-title":"Geometrical Aspects of Functional Analysis (1985\/86)","author":"J. Bourgain","year":"1987","unstructured":"J. Bourgain, On lattice packing of convex symmetric sets in R n , in Geometrical Aspects of Functional Analysis (1985\/86), Lecture Notes in Mathematics, Vol.\u00a01267, pp. 5\u201312, Springer, Berlin, 1987."},{"key":"9002_CR6","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1112\/plms\/s3-25.4.721","volume":"25","author":"G. J. Butler","year":"1972","unstructured":"G. J. Butler, Simultaneous packing and covering in Euclidean space, Proc. London Math. Soc. 25 (1972), 721\u2013735.","journal-title":"Proc. London Math. Soc."},{"key":"9002_CR7","doi-asserted-by":"crossref","first-page":"679","DOI":"10.4007\/annals.2003.158.679","volume":"158","author":"I. Daubechies","year":"2003","unstructured":"I. Daubechies and R. DeVore, Approximating a bandlimited function using very coarsely quantized data: A family of stable Sigma\u2013Delta modulators of arbitrary order, Ann. Math. 158 (2003), 679\u2013710.","journal-title":"Ann. Math."},{"key":"9002_CR8","unstructured":"S. J. Dilworth, E. Odell, T. Schlumprecht, and A. Zs\u00e1k, Partial unconditionality, Preprint, 2005."},{"issue":"1","key":"9002_CR9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.4064\/sm159-1-4","volume":"159","author":"S. J. Dilworth","year":"2003","unstructured":"S. J. Dilworth, N. J. Kalton, and D. Kutzarova, On the existence of almost greedy bases in Banach spaces, Studia Math. 159(1) (2003), 67\u2013101. (Dedicated to Professor Aleksander Pe\u0142czy\u0144ski on the occasion of his 70th birthday.)","journal-title":"Studia Math."},{"key":"9002_CR10","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s00365-002-0525-y","volume":"19","author":"S. J. Dilworth","year":"2003","unstructured":"S. J. Dilworth, N. J. Kalton, D. Kutzarova, and V. N. Temlyakov, The thresholding greedy algorithm, greedy bases, and duality, Constr. Approx. 19 (2003), 575\u2013597.","journal-title":"Constr. Approx."},{"key":"9002_CR11","volume-title":"Weakly Null Normalized Sequences in Banach Spaces","author":"J. Elton","year":"1978","unstructured":"J. Elton, Weakly Null Normalized Sequences in Banach Spaces, PhD thesis, Yale University, 1978."},{"key":"9002_CR12","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/BF02761366","volume":"40","author":"J. Elton","year":"1981","unstructured":"J. Elton, Extremely weakly unconditionally convergent series, Israel J. Math. 40 (1981), 255\u2013258.","journal-title":"Israel J. Math."},{"key":"9002_CR13","series-title":"Lecture Note Series of LMS","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1017\/CBO9780511721366.005","volume-title":"Methods in Banach Space Theory","author":"I. Gasparis","year":"2006","unstructured":"I. Gasparis, E. Odell, and Wahl, B., Weakly null sequences in the Banach spaces C(K), in Methods in Banach Space Theory (J.\u00a0M.\u00a0F.\u00a0Castello and W. B. Johnson, eds.), Lecture Note Series of LMS, Vol.\u00a0337, pp.\u00a097\u2013131, Cambridge University Press, Cambridge, 2006."},{"key":"9002_CR14","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0195-6698(92)90020-Z","volume":"13","author":"W. T. Gowers","year":"1992","unstructured":"W. T. Gowers, Lipschitz functions on classical spaces, Eur. J. Combin. 13 (1992), 141\u2013151.","journal-title":"Eur. J. Combin."},{"key":"9002_CR15","series-title":"Lecture Notes in Mathematics","first-page":"1","volume-title":"Functional Analysis (Austin, TX, 1987\/1989)","author":"R. Haydon","year":"1991","unstructured":"R. Haydon, E. Odell, and Rosenthal, H., On certain classes of Baire, 1. Functions with applications to Banach space theory, in Functional Analysis (Austin, TX, 1987\/1989), Lecture Notes in Mathematics, Vol. 1470, pp.\u00a01\u201335, Springer, Berlin, 1991."},{"key":"9002_CR16","doi-asserted-by":"crossref","first-page":"542","DOI":"10.2307\/1970663","volume":"80","author":"R. C. James","year":"1964","unstructured":"R. C. James, Uniformly non-square Banach spaces, Ann. Math. 80 (1964), 542\u2013550.","journal-title":"Ann. Math."},{"issue":"3","key":"9002_CR17","first-page":"365","volume":"5","author":"S. V. Konyagin","year":"1999","unstructured":"S. V. Konyagin and V. N. Temlyakov, A remark on greedy approximation in Banach spaces, East J. Approx. 5(3) (1999), 365\u2013379.","journal-title":"East J. Approx."},{"key":"9002_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66557-8","volume-title":"Classical Banach Spaces, I, Sequence Spaces","author":"J. Lindenstrauss","year":"1977","unstructured":"J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, I, Sequence Spaces, Springer, Berlin, 1977."},{"key":"9002_CR19","unstructured":"J. Lopez-Abad and S. Todorcevic, Pre-compact families of integers and weakly null sequences in Banach spaces, Preprint, 2005."},{"key":"9002_CR20","first-page":"150","volume":"2","author":"A. A. Milutin","year":"1966","unstructured":"A. A. Milutin, Isomorphisms of spaces of continuous functions on compacta of power continuum, Teor. Funkc. Funkc. Anal. Ih Prilo\u017e. 2 (1966), 150\u2013156 (in Russian).","journal-title":"Teor. Funkc. Funkc. Anal. Ih Prilo\u017e."},{"key":"9002_CR21","first-page":"379","volume-title":"Notes in Banach Spaces","author":"E. Odell","year":"1980","unstructured":"E. Odell, Applications of Ramsey theorems to Banach space theory, in Notes in Banach Spaces (H.\u00a0E.\u00a0Lacey, ed.), pp. 379\u2013404, University of Texas Press, Austin, 1980."},{"key":"9002_CR22","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF02398436","volume":"173","author":"E. Odell","year":"1994","unstructured":"E. Odell and T. Schlumprecht, The distortion problem, Acta Math. 173 (1994), 259\u2013281.","journal-title":"Acta Math."},{"issue":"2","key":"9002_CR23","doi-asserted-by":"crossref","first-page":"149","DOI":"10.4064\/sm-54-2-149-159","volume":"54","author":"R. I. Ovsepian","year":"1975","unstructured":"R. I. Ovsepian and A. Pe\u0142czy\u0144ski, On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in L 2, Studia Math. 54(2) (1975), 149\u2013159.","journal-title":"Studia Math."},{"issue":"3","key":"9002_CR24","doi-asserted-by":"crossref","first-page":"295","DOI":"10.4064\/sm-55-3-295-304","volume":"55","author":"A. Pe\u0142czy\u0144ski","year":"1976","unstructured":"A. Pe\u0142czy\u0144ski, All separable Banach spaces admit for every \u03b5>0 fundamental total and bounded by 1+\u03b5 biorthogonal sequences, Studia Math. 55(3) (1976), 295\u2013304.","journal-title":"Studia Math."},{"key":"9002_CR25","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1112\/jlms\/s1-25.4.327","volume":"25","author":"C. A. Rogers","year":"1950","unstructured":"C. A. Rogers, A note on coverings and packings, J. Lond. Math. Soc. 25 (1950), 327\u2013331.","journal-title":"J. Lond. Math. Soc."},{"key":"9002_CR26","doi-asserted-by":"crossref","first-page":"2411","DOI":"10.1073\/pnas.71.6.2411","volume":"71","author":"H. P. Rosenthal","year":"1974","unstructured":"H. P. Rosenthal, A characterization of Banach spaces containing \u2113 1, Proc. Nat. Acad. Sci. 71 (1974), 2411\u20132413.","journal-title":"Proc. Nat. Acad. Sci."},{"key":"9002_CR27","first-page":"707","volume":"7","author":"H. P. Rosenthal","year":"1994","unstructured":"H. P. Rosenthal, A characterization of Banach spaces containing c 0, J. Am. Math. Soc. 7 (1994), 707\u2013748.","journal-title":"J. Am. Math. Soc."},{"key":"9002_CR28","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1090\/S0002-9904-1941-07593-2","volume":"47","author":"A. Sobczyk","year":"1941","unstructured":"A. Sobczyk, Projection of the space (m) on its subspace (c 0), Bull. Am. Math. Soc. 47 (1941), 938\u2013947.","journal-title":"Bull. Am. Math. Soc."},{"key":"9002_CR29","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1006\/jath.2000.3512","volume":"107","author":"P. Wojtaszczyk","year":"2000","unstructured":"P. Wojtaszczyk, Greedy algorithm for general biorthogonal systems, J. Approx. Theory 107 (2000), 293\u2013314.","journal-title":"J. Approx. Theory"},{"key":"9002_CR30","doi-asserted-by":"crossref","first-page":"83","DOI":"10.4064\/sm-47-1-83-93","volume":"67","author":"P. Wojtaszczyk","year":"1973","unstructured":"P. Wojtaszczyk, Existence of some special bases in Banach spaces, Studia Math. 67 (1973), 83\u201393.","journal-title":"Studia Math."},{"key":"9002_CR31","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1007\/s00365-002-0505-2","volume":"18","author":"\u00d6. Yilmaz","year":"2002","unstructured":"\u00d6. Yilmaz, Stability analysis for several second-order Sigma\u2013Delta methods of coarse quantization of bandlimited functions, Constr. Approx. 18 (2002), 599\u2013623.","journal-title":"Constr. Approx."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-007-9002-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-007-9002-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-007-9002-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T07:05:09Z","timestamp":1559113509000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-007-9002-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,8,8]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["9002"],"URL":"https:\/\/doi.org\/10.1007\/s10208-007-9002-0","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,8,8]]}}}