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Weyl type theorem for operator matrices

100%

Cao X.

Studia Mathematica

2008

tom 186

nr 1

29-39

Using topological uniform descent, we give necessary and sufficient conditions for Browder's theorem and Weyl's theorem to hold for an operator A. The two theorems are liable to fail for 2 × 2 operator matrices. In this paper, we explore how they survive for 2 × 2 operator matrices on a Hilbert space.

Weyl type theorems for p-hyponormal and M-hyponormal operators

51%

Cao X., Guo M., Meng B.

Studia Mathematica

2004

tom 163

nr 2

177-188

"Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T* is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized Weyl's theorem holds for f(T), so Weyl's theorem holds for f(T), where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T). Moreover, if T* is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized a-Weyl's theorem holds for f(T) and hence a-Weyl's theorem holds for f(T).

Ograniczanie wyników

2 Studia Mathematica

2 Cao X.

1 Guo M.

1 Meng B.

1 2008

1 2004

Wyniki wyszukiwania

Weyl type theorem for operator matrices

Weyl type theorems for p-hyponormal and M-hyponormal operators