Riesz idempotent, spectral mapping theorem and Weyl's theorem for (m,n)*-paranormal operators

IF 0.3 Q4 STATISTICS & PROBABILITY Random Operators and Stochastic Equations Pub Date : 2023-07-29 DOI:10.2298/fil2110293d
S. Ram, P. Dharmarha
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引用次数: 0

Abstract

Abstract In this paper, we show that the spectral mapping theorem holds for ( m , n ) * {(m,n)^{*}} -paranormal operators. We also exhibit the self-adjointness of the Riesz idempotent E λ {E_{\lambda}} of ( m , n ) * {(m,n)^{*}} -paranormal operators concerning for each isolated point λ of σ ⁢ ( T ) {\sigma(T)} . Moreover, we show Weyl’s theorem for ( m , n ) * {(m,n)^{*}} -paranormal operators and f ⁢ ( T ) {f(T)} for every f ∈ ℋ ⁢ ( σ ⁢ ( T ) ) {f\in\mathcal{H}(\sigma(T))} . Furthermore, we investigate the class of totally ( m , n ) * {(m,n)^{*}} -paranormal operators and show that Weyl’s theorem holds for operators in this class.
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(m,n)*-超常算子的Riesz幂等性、谱映射定理和Weyl定理
摘要本文证明了(m,n)*{(m,n)^{*}}-超常算子的谱映射定理成立。我们还展示了关于σ(T){\lang1033\sigma(T)}的每个孤立点λ的(m,n)*{(m,n)^{*}}的Riesz幂等Eλ{E_。此外,我们还证明了(m,n)*{(m,n)^{*}}-超常算子的Weyl定理,以及每个f∈ℋ ⁢ (σ(T))。此外,我们还研究了一类全(m,n)*{(m,n)^{*}}-超常算子,并证明了Weyl定理适用于这类算子。
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来源期刊
Random Operators and Stochastic Equations
Random Operators and Stochastic Equations STATISTICS & PROBABILITY-
CiteScore
0.60
自引率
25.00%
发文量
24
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