{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:27:27Z","timestamp":1760059647510,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T00:00:00Z","timestamp":1750982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A pair (A,B) of Banach space operators is strict (m,X)-isometric for a Banach space operator X\u2208B(X) and a positive integer m if \u25b5A,Bm(X)=\u2211j=0mmjLAjRBj(X)=0 and \u25b5A,Bm\u22121(X)\u22600, where LA and RB\u2208B(B(X)) are, respectively, the operators of left multiplication by A and right multiplication by B. Define operators EA,B and EA,B(X) by EA,B=LARB and EA,B(X)n=EA,Bn(X) for all non-negative integers n. Using little more than an algebraic argument, the following generalised version of a result relating (m,X)-isometric properties of pairs (A1,A2) and (B1,B2) to pairs (EA1,A2(S1),EB1,B2(S2)) and (EA1,A2,EB1,B2) is proved: if Ai,Bi,Si,X are operators in B(X), 1\u2264i\u22642 and X a quasi-affinity, then the pair (EA1,A2(S1),EB1,B2(S2)) (resp., the pair (EA1,A2,EB1,B2)) is strict (m,X)-isometric for all X\u2208B(X) if and only if there exist positive integers mi\u2264m, 1\u2264i\u22642 and m=m1+m2\u22121, and a non-zero scalar \u03b2 such that I\u2212E\u03b2A1,A2(S1) is (strict) m1-nilpotent and I\u2212E1\u03b2B1,B2(S2) is (strict) m2-nilpotent (resp., (\u03b2A1,B1) is strict (m1,I)-isometric and (1\u03b2B2,A2) is strict (m2,I)-isometric).<\/jats:p>","DOI":"10.3390\/axioms14070503","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T05:29:58Z","timestamp":1751002198000},"page":"503","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["m-Isometric Operators with Null Symbol and Elementary Operator Entries"],"prefix":"10.3390","volume":"14","author":[{"given":"Bhagwati Prashad","family":"Duggal","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, P.O. 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