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Dec
15
revised Positive elements of a $C^*$ (MURPHY, ex 2-2).
added 109 characters in body
Dec
15
answered $\phi(A^+) \subset B^+$ when $\phi: A\to B$ is an isometric linear map
Dec
15
comment Positive elements of a $C^*$ (MURPHY, ex 2-2).
You used it when you said that $\sigma (a)\subset \mathbb T $ implies that $a $ is a unitary. Otherwise it is not true: $a=\begin {bmatrix}1&1\\0&1\end {bmatrix} $ has its spectrum contained in the unit circle but it is not a unitary.
Dec
15
comment Extension of linear functional on $L^1$
You show that $\|F_3\|=\|\Gamma\|_\infty $, and so the norm is achieved at the constant function $1$.
Dec
15
comment Positive elements of a $C^*$ (MURPHY, ex 2-2).
Yes you do. For non-normal operators, it is not true in general that $\|a\|=\sup\{|\lambda|:\ \lambda\in\sigma (a)\} $. For example if $a=\begin {bmatrix}0&1\\0&0\end {bmatrix} $ the left-hand-side is $1$, while the right-hand-side is $0$.
Dec
15
answered Need to show the following function is uniformly continuous on R
Dec
14
comment Positive elements of a $C^*$ (MURPHY, ex 2-2).
That would work if you knew that $a $ is normal, which a priori you don't.
Dec
14
comment Difference between an eigenvalue and a spectral value
Having an eigenvalue $\lambda $ means that $\ker (A-\lambda I)\ne\{0\} $. The $S $ in my answer has no eigenvalues (easy exercise).
Dec
14
answered Difference between an eigenvalue and a spectral value
Dec
13
revised Every infinite abelian group has at least one element of infinite order?
edited body
Dec
13
answered Every infinite abelian group has at least one element of infinite order?
Dec
13
answered Sum of odd numbers is odd if each of the natural numbers is odd
Dec
13
comment Two series with $a_n/b_n\to 1$ converges simultaneously?
nice example. I tried for a minute along that line but I didn't think of using a slow-converging term. Good job.
Dec
13
comment Two series with $a_n/b_n\to 1$ converges simultaneously?
Yes. But to really have an argument I think that you need to consider splitting the series in the series of positive terms and the series of negative terms. Annoying to write and useless in the complex case, where you would thing the same result should hold.
Dec
13
comment Two series with $a_n/b_n\to 1$ converges simultaneously?
For series with non-positive terms, I think that you need to work a little harder than that.
Dec
13
comment Studying the complex-valued function $f(z) = \frac{1}{z}$
You may want to notice that $f(1/2)=2$.
Dec
13
revised A question on the minimal tensor norm
added 1 character in body
Dec
12
answered Book suggestion to prepare the grounds for studying functional Analysis
Dec
12
answered A question on the minimal tensor norm
Dec
10
revised Creating Bratteli diagrams for Riesz groups
edited tags