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Amer. Math. Soc."],"abstract":"<p>\n                    The theory of quaternionic operators has applications in several different fields, such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and quaternionic operator theory is based on the definition of a spectrum. In fact, in quaternionic operator theory the classical notion of a resolvent operator and the one of a spectrum need to be replaced by the two\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -resolvent operators and the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -spectrum. This is a consequence of the noncommutativity of the quaternionic setting. Indeed, the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -spectrum of a quaternionic linear operator\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper T\">\n                        <mml:semantics>\n                          <mml:mi>T<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">T<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is given by the noninvertibility of a second order operator. This presents new challenges which make our approach to perturbation theory of quaternionic operators different from the classical case. In this paper we study the problem of perturbation of a quaternionic normal operator in a Hilbert space by making use of the concepts of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -spectrum and of slice hyperholomorphicity of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S\">\n                        <mml:semantics>\n                          <mml:mi>S<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">S<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -resolvent operators. For this new setting we prove results on the perturbation of quaternionic normal operators by operators belonging to a Schatten class and give conditions which guarantee the existence of a nontrivial hyperinvariant subspace of a quaternionic linear operator.\n                  <\/p>","DOI":"10.1090\/tran\/7749","type":"journal-article","created":{"date-parts":[[2018,11,26]],"date-time":"2018-11-26T09:40:39Z","timestamp":1543225239000},"page":"3257-3281","source":"Crossref","is-referenced-by-count":35,"special_numbering":"1020","title":["Perturbation of normal quaternionic operators"],"prefix":"10.1090","volume":"372","author":[{"given":"Paula","family":"Cerejeiras","sequence":"first","affiliation":[]},{"given":"Fabrizio","family":"Colombo","sequence":"additional","affiliation":[]},{"given":"Uwe","family":"K\u00e4hler","sequence":"additional","affiliation":[]},{"given":"Irene","family":"Sabadini","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2019,1,4]]},"reference":[{"key":"1","isbn-type":"print","first-page":"337","article-title":"Quaternionic quantum mechanics and noncommutative dynamics","author":"Adler, Stephen L.","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/9810228619"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1142\/S021953051650007X","article-title":"Functions of the infinitesimal generator of a strongly continuous quaternionic group","volume":"15","author":"Alpay, Daniel","year":"2017","journal-title":"Anal. 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