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2023•Linear and Multilinear AlgebraRequires access

The semi-Fredholmness and property (ω) for 2×2 upper triangular operator matrices

Jiong Dong, Xiaohong Cao

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Abstract

Let MC=(AC0B) be a 2×2 upper triangular operator matrix acting on H⊕K, where H and K are complex infinite dimensional separable Hilbert spaces. In this paper, we study the semi-Fredholmness for MC for some invertible C∈B(K,H), and using the conclusions obtained, we characterize the equivalent conditions such that MC∈(ω) for any invertible C∈B(K,H).

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What this paper is about

Let MC=(AC0B) be a 2×2 upper triangular operator matrix acting on H⊕K, where H and K are complex infinite dimensional separable Hilbert spaces. In this paper, we study the semi-Fredholmness for MC for some invertible C∈B(K,H), and using the conclusions obtained, we characterize the equivalent conditions such that MC∈(ω) for any invertible C∈B(K,H).

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Available abstract

Let MC=(AC0B) be a 2×2 upper triangular operator matrix acting on H⊕K, where H and K are complex infinite dimensional separable Hilbert spaces. In this paper, we study the semi-Fredholmness for MC for some invertible C∈B(K,H), and using the conclusions obtained, we characterize the equivalent conditions such that MC∈(ω) for any invertible C∈B(K,H).

Key concepts: Invertible matrix, Mathematics, Triangular matrix, Operator matrix, Operator (biology), Separable space, Pure mathematics, Matrix (chemical analysis)

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