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Apr
7
comment What is bi-infinite matrix?
A sequence labelled by the integers (instead of just the natural numbers) is sometimes called a bi-infinite sequence (it has infinitely many entries in both the positive and negative directions). So perhaps a bi-infinite matrix is one whose elements are labelled by integers. That is, it is of the form $(a_{mn})$ where $m, n \in \mathbb Z$.
Apr
5
comment Support and range projections in von Neumann algebra
Compare the support and range projections with $p$ and $1-p$. As $p$ and $1-p$ are orthogonal, so too are the support and range projections of $pm(1-p)$.
Mar
22
awarded  Yearling
Mar
21
answered polynomial series and root multiplicity
Mar
20
comment What's wrong in this reasoning of $l_\infty$ separability?
Many different functionals on $\ell_\infty$ will restrict to the same functional on $c_0$. That is, there exist $f, g \in \ell_\infty^*$ such that $f \neq g$ but $f|_{c_0}=g|_{c_0}$. In fact for each $f$ there will be infinitely many $g$ which have the same restriction to $c_0$ as $f$.
Mar
14
comment $n^n$ are the moments of a measure on the non-negative real line?
You may be interested in en.wikipedia.org/wiki/Stieltjes_moment_problem
Mar
13
comment Computing an induced matrix norm
You first need to specify the norm on your vector space. Is $\Vert x \Vert$ the usual Euclidean norm on $\mathbb R^n$ or $\mathbb C^n$? In this case, the induced norm is equal to the largest singular value of $A$. See here for further details.
Mar
12
revised Is this proof valid for showing that this normed vector space is a Banach space?
added 483 characters in body
Mar
12
comment Is this proof valid for showing that this normed vector space is a Banach space?
@Joshua Well, I did say "or a similar one", so if you add extra details like you did, there is, of course, no problem. Also, I was interpreting the question more broadly than you: is there in general a problem with changing the norm when you are trying to show completeness?
Mar
12
answered Is this proof valid for showing that this normed vector space is a Banach space?
Mar
10
answered A proposition about cyclic representation in C*-algebra
Mar
7
revised A simple question about positive element in C*-algebra
added 12 characters in body
Mar
7
answered An exercise in operator theory
Mar
7
answered A simple question about positive element in C*-algebra
Feb
11
answered An inequality for completely positive maps.
Dec
17
revised prove that T is normal if and only if $T= T_1 + iT_2$
Added LaTeX
Dec
17
awarded  Custodian
Dec
17
reviewed Reviewed Spanning sets in linear block codes
Dec
17
suggested suggested edit on prove that T is normal if and only if $T= T_1 + iT_2$
Dec
17
comment prove that T is normal if and only if $T= T_1 + iT_2$
As $T_1$ and $T_2$ are selfadjoint, $T^*=T_1 - i T_2$. Now compare $T^*T$ with $TT^*$.