On the generalized Hadamard product and the Jordan-Hadamard product

The generalized Hadamard product S * T and the Jordan-Hadamard product S ∘ T of two operator-matrices S and T are introduced. They coincide with the usual Hadamard product of two complex matrices when the underlying Hilbert spaces are one-dimensional. Some inequalities which hold true for the usual...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1980-12, Vol.22 (3), p.321-337
Main Authors: Chuan, Jen-chung, Chuan, Wai-fong
Format: Article
Language:English
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Summary:The generalized Hadamard product S * T and the Jordan-Hadamard product S ∘ T of two operator-matrices S and T are introduced. They coincide with the usual Hadamard product of two complex matrices when the underlying Hilbert spaces are one-dimensional. Some inequalities which hold true for the usual Hadamard product of positive definite complex matrices are shown to be true for these two new products of positive invertible operator-matrices.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700006663