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On the generalized Hadamard product and the Jordan-Hadamard product

Published online by Cambridge University Press:  17 April 2009

Jen-chung Chuan  and
Wai-fong Chuan
Jen-chung Chuan
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China.
Wai-fong Chuan
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 3 , December 1980 , pp. 321 - 337
Copyright
Copyright © Australian Mathematical Society 1980

References

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