On Weyl's Theorem for Quasi-Class a Operators

WEYL'S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T*k|T2|Tk≥T*k|T|2Tk

“…In [14], W. Y. Lee and S. H. Lee showed that if T ∈ B(H) is a hyponormal operator and f ∈ H(σ(T )), then Weyl's theorem holds for f (T ). Recently, this result was extended to p-quasihyponormal operators, class A operators and quasi-class A operators in [19], [18] and [5], respectively. In this section we show that if T ∈ B(H) is a quasi-class (A, k) operator and f ∈ H(σ(T )), then Weyl theorem holds for f (T ).…”

“…In [14], W. Y. Lee and S. H. Lee showed that if T is hyponormal operator, then Weyl's theorem holds for f (T ), where f is an analytic function on a neighborhood of spectrum of T . Recently, this result was extended to p-quasihyponormal operators, class A operators and quasi-class A operators in [19], [18] and [5], respectively.…”

Conditions Implying Self-adjointness of Operators

“…It is well known that any p-hyponormal operator is q-hyponormal for q ≤ p by Löwner's theorem. Recall [10,11] that an operator T ∈ B(H) is called quasi-class A operator if T * |T 2 |T ≥ T * |T | 2 T . Quasi-class A operator is an extension of p-hyponormal operator, class A operator (i.e., |T 2 | − |T | 2 ≥ 0)(see [3,7]) and p-quasihyponormal operator (i.e., T * (|T | 2p − |T * | 2p )T ≥ 0)(see, [2,6,12]).…”

Weyl's Type Theorems for Quasi-Class A Operators

“…It is known that if T∈B(H) then a-Browder's theorem implies Browder's theorem. In [8] , the authors proved that Weyl's theorem holds for quasi-classA, in this paper, we prove that generalized Weyl's holds for quasi-class A operators.…”

“…The class of quasi-class A introduced and studied by Jeon and Kim [15] , for more interesting properties the reader should refer to [8,15] . Recall that an operator S∈B(H) is said to be quasiaffine transform of T (abbreviate S T ) if there is a quasiaffinity X such that XS = TX.…”