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Prove that $P_{M^{\perp }}=P_M^{\perp }$.

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#functional-analysis #hilbert-spaces
92
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Brezis' exercise 6.24.1: prove that $T$ is positive IFF $\sigma (T) \subset [0, \infty)$

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#functional-analysis #solution-verification #hilbert-spaces #spectral-theory #adjoint-operators
245
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About the square root of a positive operator

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#functional-analysis #analysis #proof-explanation #operator-theory #hilbert-spaces
37
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Why does unitary representation have $G$-invariant subspace necessarily?

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#representation-theory #hilbert-spaces
42
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Brezis' exercise 6.24.3: prove that $(0,1) \subset \rho(T)$ IFF $\langle Tu, u \rangle \leq |T u|^2$ for all $u\in H$

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#functional-analysis #solution-verification #hilbert-spaces #spectral-theory #adjoint-operators
93
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Is there any guarantee that a norm one operator, $T$ will attain its norm at some extreme point?

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#functional-analysis #operator-theory #hilbert-spaces #banach-spaces
89
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Solving an equation in a Hilbert space

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#hilbert-spaces #inner-products
114
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What does nonlinear mapping $\Phi(x)$ mean? Is it a vector or matrix?

Published on
#matrices #hilbert-spaces #reproducing-kernel-hilbert-spaces
21
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About homotopies from rotation Matrizes

Published on
#hilbert-spaces #homotopy-theory
117
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Reference Request for Schatten Class Operators being an ideal in the set of Bounded operators.

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#functional-analysis #reference-request #hilbert-spaces
48
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Is there non-zero vector with bounded orbit if the set of vectors with unbounded is residual and open in Banach space $X$?

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#real-analysis #functional-analysis #operator-theory #hilbert-spaces #banach-spaces
62
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Compact operator on Hilbert space: clarification of Wikipedia article

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#hilbert-spaces #spectral-theory #compact-operators
37
Views

Proof of multiplicativity of spectral measures

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#hilbert-spaces #spectral-theory
35
Views

Does the vector space of differences of quantile functions have a neat characterization?

Published on
#convex-analysis #hilbert-spaces #convex-cone #total-variation #quantile-function
81
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Implication of mean ergodic theorem

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#measure-theory #operator-theory #hilbert-spaces #ergodic-theory #unitary-matrices

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