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Upper triangular operator matrices with the single-valued extension property
Authors:B.P. Duggal
Affiliation:8 Redwood Grove, Northfield Avenue, Ealing, London W5 4SZ, United Kingdom
Abstract:If A=(Aij)1?i,j?nB(X) is an upper triangular Banach space operator such that AiiAij=AijAjj for all 1?i?j?n, then A has SVEP or satisfies (Dunford's) condition (C) or (Bishop's) property (β) or (the decomposition) property (δ) if and only if Aii, 1?i?n, has the corresponding property.
Keywords:Banach space   Upper triangular operator   SVEP   Bishop's property   mmlsi9"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0022247X08008482&  _mathId=si9.gif&  _pii=S0022247X08008482&  _issn=0022247X&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=da005f8a4b6c38308ea5f60f0728fa90')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >(β)   Decomposition property   mmlsi10"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0022247X08008482&  _mathId=si10.gif&  _pii=S0022247X08008482&  _issn=0022247X&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=a7fa5746c6fe17114368a62a059b1a46')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >(δ)   Quasi-nilpotent equivalent
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