Locally Convex Spaces (Graduate Texts in Mathematics Book 269) 2014th Edition by M. Scott Osborne (PDF)

Description

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 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A very readable introduction to locally convex spaces.

⭐The best book about Locally Convex Space I have ever seen! It is a treasure for everyone who wishes to capture the understanding of what a Locally Convex Space means.

⭐Convex SpacesSpringer New York, Berlin HeidelbergJoseph J Grenier MD PhDThis is a great book about the set theory of real and complex numbers in addition to being a good reference on topological vector spaces. I recommend it to all logicians and philosophers of logic. It should appeal to abstract mathematicians, students at the undergraduate/ and graduate levels.

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