New posts in Hilbert Spaces

What does it mean for an operator to be diagonal with respect to an orthonormal basis?

Example of infinite dimensional linear spaces where the space is equal to its dual.

If $A$ is a self-adjoint operator . Is $\|A^n\|=\|A\|^n,\;\forall n$?

Hilbert space basis which is not a vector space basis

Why $\displaystyle\lim_{n\to+\infty}x_n\otimes y_n=x\otimes y\;?$

Is every self-adjoint operator bounded?

$\langle Tu\;|\;u\rangle=0,\;\forall u\in E \Longrightarrow T=0$?

Self-adjoint operator as difference of two positive operators

Characterization of Parseval Frame

Is every Hilbert space separable?