Advanced techniques with block matrices of operators [r-libre/3820]

Morneau-Guérin, Frédéric (2025). Advanced techniques with block matrices of operators [review of the book from Moslehian, Mohammad Sal, & Osaka, Hiroyuki]. zbMATH Open.

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Item Type:	Book Reviews
Refereed:	Yes
Status:	Published
Abstract:	Advanced Techniques with Block Matrices of Operators by Mohammad Sal Moslehian and Hiroyuki Osaka is a research-level monograph that offers an excellent, modern, and relatively self-contained resource for readers with a solid background in operator theory. The opening chapter provides a dense yet concise refresher on foundational tools from functional analysis, operator theory, and matrix analysis. While it briefly introduces elementary notions (such as norms and Hilbert spaces) it quickly moves on to more advanced concepts like the Gelfand-Beurling formula and a sketch of the Gelfand-Naimark-Segal representation. This chapter is not intended as a textbook for introductory courses; rather, it presupposes substantial familiarity with the rudiments of functional analysis and operator theory. It continues with key results such as Douglas’ majorization theorem and the polar decomposition, followed by three useful digressions: one on unitarily invariant norms, one on the Moore-Penrose inverse, and one clarifying the distinction between real and complex Hilbert spaces.
Additional Information:	© FIZ Karlsruhe GmbH 2025. ALL RIGHTS RESERVED.
Official URL:	https://zbmath.org/7925392
Depositor:	Morneau-Guérin, Frédéric
Owner / Manager:	Frédéric Morneau-Guérin
Deposited:	24 Jul 2025 13:24
Last Modified:	24 Jul 2025 13:24

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