ALLAN, GRAHAM R.
Introduction to Banach Spaces and Algebras (Oxford Graduate Texts in Mathematics 20)
Oxford: Oxford University Press, 2011. First Edition; First Impression. Original decorated wrappers. ISBN: 0199206546. Spine uncreased. Light wear to spine, covers & corners. ; "Introduction to Banach Spaces and Algebras" by Graham R. Allan, is an advanced mathematics textbook focusing on the fundamental aspects of functional analysis. It is primarily aimed at final year undergraduate or early graduate students who have a background in basic mathematical concepts like metric spaces and complex analysis, but not necessarily in Lebesgue integration. The book starts with the essentials of Banach spaces, exploring topics such as dual spaces and bounded linear operators. It thoroughly covers key theorems of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems, which establish a foundation for further study in this field. A significant portion of the text is dedicated to the theory of Banach algebras, with a detailed discussion on the holomorphic functional calculus for both single and several variables. This includes comprehensive background theory and numerous examples and applications, particularly in the context of Fourier series and operators on Hilbert spaces. The textbook is well-structured to facilitate understanding, featuring exercises to test comprehension and extensive notes that guide readers towards more advanced topics. Edited posthumously by Professor H. G. Dales after Allan's death, the book reflects a careful and rigorous approach to a complex subject. ; Octavo; viii, 371 pages. Near Fine with no dust jacket .
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Keywords: 0199206546 Algebra