I am studying geometry of Banach spaces and applications in metric fixed point theory. Does anyone have a good recommendation of books//lectures/resources/etc.? Thanks.
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Martin Sleziak
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user62498
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if you are looking for fixed point theory you should look into the direction of non-linear functional analysis – Norbert Aug 17 '14 at 15:14
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I am studding geometry of Banach spaces and sometimes I like know applications of geometry of Banach spaces – user62498 Aug 17 '14 at 15:43
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These are the books I recommend:
A short course on Banach space theory. N. L. Carothers. A friendly introduction into geometry of Banach spaces
An Introduction to Banach Space Theory Graduate Texts in Mathematics. Robert E. Megginson. A more academic, but still very basic exposition.
Topics in Banach space theory. F. Albiac, N. Kalton. Though this is still a textbook, it contains a lot. Mostly for future Banach space specialists.
The isometric theory of classical Banach spaces. H. E. Lacey. If you are interesed geometric effects concerned with exact value of the norm.
Banach space theory. The basis for linear and non-linear analysis. M. Fabian, P. Habala, P. Hajek, V. Montesinos, V. Zizler. It is more an encyclopedia than a textbook. Contains much more than you ever want to know.
Norbert
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Thank you, this answer is very helpful! Although "contains much more than you ever want to know": Probably not because I want to know everything ;) – Mar 05 '15 at 23:34
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