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Questions related from Mohammed Hichem Mortad
Let \( A \) and \( B \) be two square matrices. It is well-known that the equation \( AB = I \) is equivalent to \( BA = I \). This equivalence holds even for matrices whose entries lie in a...
07 December 2024 9,579 3 View
Let $T\in B(H)$. Assume that $T^3$ is normal, i.e., $T^{*3}T^3=T^3T^{*3}$. When is $T^2$ normal? Here is a known related result: Also, if $T^2$ is normal and $T$ has a positive real part, then...
18 June 2024 5,786 0 View
Let $A$ and $B$ be two unbounded self-adjoint (+ positive if needed) operators with domains $D(A)$ and $D(B)$ respectively. By the spectral theorem, we know that $A=\int_{\mathbb{R}}\lambda dE$...
07 September 2023 5,308 0 View
Is $TT^*$ (or $T^*T$) densely defined if $T$ is a densely defined and symmetric linear operator? I feel this is untrue, but do you have a counterexample? Thanks, Hichem
17 February 2022 6,745 12 View
Let $A$ be a densely defined symmetric (unclosed) operator and let $B\in B(H)$ be positive. I know that if $\overline{A}B$ is normal, then $AB$ need not be normal. My question is: If $AB$ is...
31 January 2022 8,682 2 View
Let $B\in B(H)$ be self-adjoint and let $A$ be a densely defined symmetric (and closed if needed) operator such that $A^2$ is densely defined. If $BA^2\subset A^2B$ say, is there a result which...
29 January 2022 9,390 8 View
Hi Let HH be a Hilbert space. Let S∈B(H) and let T be a densely defined closed operator such that TS⊂ST. Assume further that T is boundedly invertible and that both S and T are self-adjoint and...
15 January 2022 9,505 10 View
Dear colleagues Do you think all journals should use a double-blind review? That is, authors will be unknown to referees and vice versa. Most of the journals use the classical review in which...
01 January 1970 7,052 2 View
