Inner product inequalities with applications

In this paper, we show some inner product inequalities, which can be considered of Cauchy-Schwarz and Buzano type inequalities for Hilbert space operators. This will lead to several applications that include a new equivalent statement to the fact that an operator matrix is positive and new upper bou...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 73; no. 9; pp. 2089 - 2102
Main Authors Sababheh, Mohammad, Moradi, Hamid Reza, Sahoo, Satyajit
Format Journal Article
LanguageEnglish
Published Taylor & Francis 13.06.2025
Subjects
Buzano's inequality
Cauchy-Schwarz inequality
numerical radius
operator norm
Primary 47A12
Secondary 47B10
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Summary:In this paper, we show some inner product inequalities, which can be considered of Cauchy-Schwarz and Buzano type inequalities for Hilbert space operators. This will lead to several applications that include a new equivalent statement to the fact that an operator matrix is positive and new upper bounds for the numerical radius.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2024.2312444