Let H be a Hilbert space. For any subset A of ,H define . A ⊥ If ,H A ⊆ B ⊆ then show that:
i) B¹⊆ A
ii) A ⊆ A ^⊥⊥
State conditions on A^⊥⊥ =A

Posted on : 2023-12-02 22:39:12 | Author : IGNOU Academy | View : 73

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Functional analysis is a branch of mathematics that deals with infinite-dimensional vector spaces and their transformations. In the context of a Hilbert space H, the orthogonal complement of a subset A, denoted by A⊥, consists of all vectors ________ _________ _________ ___ ____________ _____________ ______ ____________ ___________ __.
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Degree : MASTER DEGREE PROGRAMMES
Course Name : M.Sc. Mathematics with Applications in Computer Science
Course Code : MSCMACS
Subject Name : Functional Analysis
Subject Code : MMT 6
Year : 2023

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Let H be a Hilbert space. For any subset A of ,H define . A ⊥ If ,H A ⊆ B ⊆ then show that:

i) B¹⊆ A

ii) A ⊆ A ^⊥⊥

State conditions on A^⊥⊥ =A

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Let H be a Hilbert space. For any subset A of ,H define . A ⊥ If ,H A ⊆ B ⊆ then show that: i) B1⊆ Aii) A ⊆ A ⊥⊥State conditions on A⊥⊥ =A

Related Question

Let H be a Hilbert space. For any subset A of ,H define . A ⊥ If ,H A ⊆ B ⊆ then show that:
i) B¹⊆ A
ii) A ⊆ A ^⊥⊥
State conditions on A^⊥⊥ =A