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10 Questions

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3	For $T$ compact, $I-T$ left or right invertible implies $I-T$ invertible
2	Help with proving: If $X$ is a Hilbert $A$-$B$-module, then $ \\| _A \langle x,x \rangle \\| = \\| \langle x,x \rangle _B \\| $ for all $x\in X $.
2	Trying to prove: Let $E$ be a Hilbert $A$-module. Then, $E\langle E,E\rangle $ is norm dense in $E$.
2	If $X$ is reflexive, $T\in B(X,Y)$ and $\\| Tx_n - Tx \\| \rightarrow 0$ whenever $x_n \rightarrow x$ weakly then $T$ is compact.
2	Function in $\mathcal{C}(X\times Y)$ can be “approximated” by sum of finite number of functions of the form $g(x)h(y)$

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74 Reputation

+5	How to prove: Every non-degenerate representation $\{ \pi , H \} $ of an involutive Banach algebra is a direct sum of cyclic representations.
+10	Help with proving: If $X$ is a Hilbert $A$-$B$-module, then $ \\| _A \langle x,x \rangle \\| = \\| \langle x,x \rangle _B \\| $ for all $x\in X $.
+5	For $T$ compact, $I-T$ left or right invertible implies $I-T$ invertible
+5	Trying to prove: Let $E$ be a Hilbert $A$-module. Then, $E\langle E,E\rangle $ is norm dense in $E$.

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14 Tags

0 functional-analysis × 9	0 functions
0 c-star-algebras × 3	0 inner-product-space
0 modules × 3	0 hilbert-spaces
0 analysis × 2	0 compact-operators
0 operator-theory × 2	0 inverse

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$Mathematics Stack Exchange$

Mathematics

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