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Locally Convex Spaces (Graduate Texts In Mathematics)

For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert space...

Series: Graduate Texts in Mathematics (Book 269)
Hardcover: 213 pages
Publisher: Springer; 2014 edition (November 7, 2013)
Language: English
ISBN-10: 3319020447
ISBN-13: 978-3319020440
Product Dimensions: 6.1 x 0.6 x 9.2 inches
Amazon Rank: 3444234
Format: PDF Text TXT ebook

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“A very readable introduction to locally convex spaces....”

are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis.While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.