New posts in Operator Theory

C$^{*}$-algebra acting irreducibly on the finite-dimensional space $\mathbb{C}^{n}$ must be $M_{n}(\mathbb{C})$

Quasinilpotent operators satisfying a polynomial identity

A cylinder in infinite-dimensional Hilbert space cannot be homeomorphic to a sphere

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

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

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

Convergence of $A_nT$ to $AT$ in operator norm for compact $T$

Finding the spectral family of $A^2$