Jiong Dong, Xiaohong Cao
Abstract
Let H and K be complex infinite dimensional separable Hilbert spaces. For given operators A∈B(H) and B∈B(K), we provide necessary and sufficient conditions which make a 2×2 upper triangular operator matrix MC=(AC0B) a CFI operator for some (or every) C∈B(K,H).
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Let H and K be complex infinite dimensional separable Hilbert spaces. For given operators A∈B(H) and B∈B(K), we provide necessary and sufficient conditions which make a 2×2 upper triangular operator matrix MC=(AC0B) a CFI operator for some (or every) C∈B(K,H).
Key concepts: Mathematics, Operator matrix, Triangular matrix, Operator (biology), Separable space, Quasinormal operator, Multiplication operator, Compact operator