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You searched IISERK - Title: Crash [videorecording] : a tale of two species / prodced by Argo Films and Thirteen/WNET New York ; written, produced, and directed by Allison Argo.
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Call Number
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515.7
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Author
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Voigt, Jürgen. author.
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Title
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A Course on Topological Vector Spaces [electronic resource] / by Jürgen Voigt.
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Material Info.
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VIII, 155 p. 1 illus. in color. online resource.
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Series
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Compact Textbooks in Mathematics, 2296-455X
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Series
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Compact Textbooks in Mathematics, 2296-455X
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Summary Note
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This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians. .
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Notes
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Initial topology, topological vector spaces, weak topology -- Convexity, separation theorems, locally convex spaces -- Polars, bipolar theorem, polar topologies -- The theorems of Tikhonov and Alaoglu-Bourbaki -- The theorem of Mackey-Arens -- Topologies on E'', quasi-barrelled and barrelled spaces -- Reflexivity -- Completeness -- Locally convex final topology, topology of D(\Omega) -- Precompact -- compact – complete -- The theorems of Banach--Dieudonne and Krein—Smulian -- The theorems of Eberlein--Grothendieck and Eberlein—Smulian -- The theorem of Krein -- Weakly compact sets in L_1(\mu) -- \cB_0''=\cB -- The theorem of Krein—Milman -- A The theorem of Hahn-Banach -- B Baire's theorem and the uniform boundedness theorem.
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ISBN
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9783030329457
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Subject
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Functional analysis.
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Subject
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Functional analysis.
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Added Entry
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SpringerLink (Online service)
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Date
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Year, Month, Day:02110081
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