New posts in hilbert-spaces

In a Hilbert space $X$, $T \in B(X)$, $|\lambda|=\lVert T \rVert$. Prove that $Im(\lambda I - T)+Ker(\lambda I-T)$ is dense in $X$

functional-analysis hilbert-spaces

$L^p$-space is a Hilbert space if and only if $p=2$

real-analysis functional-analysis measure-theory hilbert-spaces banach-spaces

No trace on $B(H)$ if $H$ is infinite dimensional

functional-analysis hilbert-spaces operator-algebras von-neumann-algebras

Orthonormal Basis for Hilbert Spaces

linear-algebra functional-analysis hilbert-spaces orthonormal

Parallelogram / Polarization Inequality

real-analysis functional-analysis multivariable-calculus inequality hilbert-spaces

$\|T\| \leq\|T\|_{0}^{1 / 2}\left\|T^{*}\right\|_{0}^{1 / 2}$ for compact operators on Hilbert spaces.

functional-analysis operator-theory hilbert-spaces compact-operators self-adjoint-operators

A sequence that converges weakly but not in the Cesàro sense

functional-analysis convergence-divergence hilbert-spaces weak-convergence

What is the use of Spectral Theorem?

hilbert-spaces operator-theory spectral-theory operator-algebras

Spectrum proofs

functional-analysis hilbert-spaces spectral-theory

Computing the Fourier transform of $H_k(x)e^{-x^2/2}$, where $H_k$ is the Hermite polynomial.

fourier-analysis power-series hilbert-spaces fourier-transform hermite-polynomials

Trace of non-negative self-adjoint integral operator

functional-analysis operator-theory hilbert-spaces trace

Non-examples for the Kato-Rellich Theorem

linear-algebra functional-analysis partial-differential-equations hilbert-spaces examples-counterexamples

The inner product of the Cartesian Product space

analysis hilbert-spaces

Prob. 8, Sec. 3.5 in Erwin Kreyszig's Introductory Functoinal Anlaysis With Applications

real-analysis analysis functional-analysis hilbert-spaces inner-products

Is ultraproduct of separable Hilbert space is separable?

functional-analysis set-theory hilbert-spaces operator-algebras

Convergence in weak topology implies convergence in norm topology

functional-analysis hilbert-spaces weak-convergence

Prove : If $\sum_na_nb_n$ converges whenever $\sum b_n^2 \lt \infty,$ then $\sum a_n^2<\infty$

real-analysis functional-analysis hilbert-spaces banach-spaces

Vector space that can be made into a Banach space but not a Hilbert space

hilbert-spaces banach-spaces

Does the shift operator on $\ell^2(\mathbb{Z})$ have a logarithm?

linear-algebra functional-analysis hilbert-spaces quantum-mechanics

Conjecture: the function $d(x, y):=\frac{||x-y||}{\max(||x||, ||y||)}$ is a distance

metric-spaces hilbert-spaces