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Norm of a linear combination of two operators on a Hilbert space

Published online by Cambridge University Press:  17 April 2009

Takahiko Nakazi  and
Takanori Yamamoto
Takahiko Nakazi
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060–0810Japan e-mail: nakazi@math.sci.hokudai.ac.jp
Takanori Yamamoto
Affiliation:
Department of Mathematics, Hokkai-Gakuen UniversitySapporo 062–8605Japan e-mail: yamatk@hucc.hokudai.ac.jp
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Abstract

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Let α, β γ, δ be complex numbers such that γδ ≠ 0. If A and B are bounded linear operators on the Hilbert space H such that γA + δB is right invertible then we study the operator norm of (αA + βB)(γA + δB)−1 using the angle φ between two subspaces ran A and ran B or the angle ψ = ψ(A, B) between two operators A and B where

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 9 - 22
Copyright
Copyright © Australian Mathematical Society 2002

References

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