New posts in Hilbert Spaces

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

Orthogonal Projection onto the $ {L}_{1} $ Unit Ball

Is there an injective operator with a dense nonclosed one-codimensional range?

Showing $T$ is continuous.

Is the number of dimensions in Hilbert Space countable infinity or uncountable infinity?

Is it mathematically problematic to consider the complex space of real(!)-valued functions?

Fock space used in Quantum mechanic : how can we have direct sum of spaces of different dimensions?

Definition of Essentially Self Adjoint Operators

Why weak convergence doesn't imply convergence?

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