ON RANK-ONE ? *-COMMUTING OPERATORS
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2014, Vol 9, Issue 5
Abstract
Let ? be a non zero complex number. An operator A is a rank one ? *-commutes with B if AB - ? BA* has rank one. If, moreover, B is compact operator then A is called to belong to (H). In other words,(H) = fA 2 B(H)jAB-? BA* has rank one for some compact operator B} . We study the basic properties of (H). We prove that if A 2 B(H) has an eigenvalue dierent than? , and A has a fixed point then (H).
Authors and Affiliations
Nuha Hamada
Keywords
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- DOI 10.24297/jam.v9i5.2345
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