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WEYL’S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T *k|T 2|T k≥T *k|T |2T k

김인현
대한수학회 (The Korean Mathematical Society)|2010.03|대한수학회지 (Journal of the KMS)|제47권 제2호|pp. 351-361

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참고문헌

키워드

tensor productquasi-class (Ak) operatorWeyl’s theorem
주제분류수학

초록

For a bounded linear operator T on a separable complex infinite dimensional Hilbert space H, we say that T is a quasi-class (A, k)operator if T *k|T 2|T k≥T *k|T |2T k. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl’s theorem. Also, we consider the tensor product for quasi-class (A, k) operators.

Abstract

For a bounded linear operator T on a separable complex infinite dimensional Hilbert space H, we say that T is a quasi-class (A, k)operator if T *k|T 2|T k≥T *k|T |2T k. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl’s theorem. Also, we consider the tensor product for quasi-class (A, k) operators.

참고문헌 (20)

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