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RKC
  • Member for 2 years, 9 months
  • Last seen more than 1 year ago
6 votes
1 answer
271 views

Proving an inequality for operators.

5 votes
2 answers
386 views

If $\lambda \in \partial \sigma (T)$ then $T - \lambda$ cannot be surjective.

4 votes
2 answers
252 views

Is Haar measure reflection invariant?

3 votes
2 answers
176 views

Question on non-unital finite dimensional Banach algebras.

3 votes
0 answers
54 views

Proving that $\varphi$ is operator convex.

3 votes
0 answers
46 views

Question on an inequality concerning integrals.

2 votes
1 answer
217 views

If $A$ is a non-unital $C^*$-algebra then $\widehat {A}$ can never be compact with respect to the Gelfand topology.

2 votes
0 answers
49 views

Show that $\partial \sigma (T) \subseteq \sigma_{\text{ap}} (T).$

2 votes
1 answer
79 views

Question on charaterization of the parts of the spectrum of an operator.

2 votes
1 answer
70 views

How to show that the sequence $\{T (e_n)\}_{n \geq 1}$ is square summable?

2 votes
1 answer
27 views

Prove or disprove the following statement on the spectrum of $p(A,A^*).$

2 votes
0 answers
76 views

Find the value of $\lim\limits_{n \to \infty} \left(1+\frac{C_0}{C_1}\right)\left(1+\frac{C_1}{C_2}\right)\cdots\left(1+\frac{C_{n-1}}{C_n}\right).$

2 votes
1 answer
109 views

Find the maximum value of $x$ for which $\lim\limits_{n \to \infty} a_n(x)$ exists. [closed]

2 votes
0 answers
161 views

What are the maximal ideals of $C_0 (X),$ where $X$ is a locally compact Hausdorff space?

1 vote
1 answer
48 views

How to show that $\overline {f}$ is continuous on $\widehat {A} \cup \{\varphi_{0}\}\ $?

1 vote
0 answers
46 views

Question on determining the region of convergence and uniform convergence of a series.

1 vote
1 answer
130 views

Determining non-zero multiplicative linear functionals on $C_0(X).$

1 vote
2 answers
197 views

Find the order of $2$ in the multiplicative group $(\mathbb Z/151\ \mathbb Z)^{\times}.$

1 vote
0 answers
55 views

Showing that $\sigma_A (a) = \sigma_C (A).$

1 vote
1 answer
59 views

Showing that $a \in \text {GL} (A).$

1 vote
1 answer
62 views

Show that the map $\varphi : \chi \to \psi_{\chi}$ is continuous.

1 vote
1 answer
170 views

Question on the spectral theorem for unitary operators.

1 vote
1 answer
53 views

How do I show that $\frac {|s|} {\sigma} \leq \sqrt {1 + \tan \left (\frac {\pi} {2} - \delta \right )}\ $?

1 vote
1 answer
25 views

Can we conclude that $g \in C_c (V)\ $?

1 vote
1 answer
252 views

Showing that $C_0 (X)^{+} \cong C_0 (X^{+}).$

1 vote
1 answer
70 views

Showing that $\lim \sup\limits_{\gamma} \left \|a - a e_{\gamma} \right \| \leq \|a - b\|$ for all $a \in A$ and $b \in J.$

1 vote
1 answer
71 views

On existence of a bounded linear functional $f.$

0 votes
1 answer
152 views

Uniform convergence of $\prod\limits_{n=1}^{\infty} \left (1 - \frac {z} {n} \right )$ on compact sets.

0 votes
2 answers
64 views

What can be said about $a_n\ $?

0 votes
1 answer
190 views

$C$ is convex and norm closed $\implies C$ is weakly closed.