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Antinormal operators and antinormality of composition operators on $L^2(X)$

Harish Chandra|Arvind Bhatt
대한수학회 (The Korean Mathematical Society)|2024.10|대한수학회논문집 (Communications of the KMS)|제39권 제4호|pp. 839-849|DOI 10.4134/CKMS.c230167

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키워드

Composition operatorantinormal operatorindex of an operatorFredholm operator
주제분류수학

초록

In this article, we show that if $T\in \mathcal{B}(H)$ is an antinormal operator, $M$ is a reducing subspace for $T$ and $i(T|_M)$ and $i(T)$ are of the same sign, then $T|_M$ is also antinormal. We also characterize the antinormality of composition operators on $L^2(X)$ for a $\sigma$-finite measure space $X$.

Abstract

In this article, we show that if $T\in \mathcal{B}(H)$ is an antinormal operator, $M$ is a reducing subspace for $T$ and $i(T|_M)$ and $i(T)$ are of the same sign, then $T|_M$ is also antinormal. We also characterize the antinormality of composition operators on $L^2(X)$ for a $\sigma$-finite measure space $X$.

참고문헌 (19)

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