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Titlebook: Notes on Functional Analysis; Rajendra Bhatia Book 2009 Hindustan Book Agency (India) 2009

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发表于 2025-3-21 16:41:37 | 显示全部楼层 |阅读模式
书目名称Notes on Functional Analysis
编辑Rajendra Bhatia
视频video
丛书名称Texts and Readings in Mathematics
图书封面Titlebook: Notes on Functional Analysis;  Rajendra Bhatia Book 2009 Hindustan Book Agency (India) 2009
描述These notes are a record of a one semester course on Functional Analysis given by the author to second year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space. The book is organised as twenty six lectures, each corresponding to a ninety minute class session. This may be helpful to teachers planning a course on this topic. Well prepared students can read it on their own.
出版日期Book 2009
版次1
doihttps://doi.org/10.1007/978-93-86279-45-3
isbn_ebook978-93-86279-45-3
copyrightHindustan Book Agency (India) 2009
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Dimensionality,Let . be a vector space and let . be a subset of it. We say . is . if for every finite subset {.,…, .} of ., the equation.holds if and only if . = . = ⋯ = . = 0. A (finite) sum like the one in (2.1) is called a . of .,…, ..
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New Banach Spaces from Old,Let . be a vector space and . a subspace of it. Say that two elements . and . of . are ., . ~ ., if . − . ∈ .. This is an equivalence relation on .. The coset of . under this relation is the set..Let . be the collection of all these cosets. If we set.then . is a vector space with these operations.
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The Uniform Boundedness Principle,The . says that a complete metric space cannot be the union of a countable number of nowhere dense sets. This has several very useful consequences. One of them is the Uniform Boundedness Principle (U.B.P.) also called the ..
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Dual Spaces,The idea of duality, and the associated notion of adjointness, are important in functional analysis. We will identify the spaces .* for some of the standard Banach spaces.
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The Second Dual and the Weak* Topology,The dual of .* is another Banach space .**. This is called the . or the . of .. Let . be the map from . into .** that associates with . ∈ . the element . ∈ .** defined as. Then . is a linear map and ‖.‖ = ‖.‖. (See (9.2).) Thus . is an . and we can regard . as a subspace of .**.
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Orthonormal Bases,A subset . in a Hilbert space is said to be an . if 〈., .〉 = 0 for all ., . in . (. ∈ .), and ‖.‖ = 1 for all . in ..
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