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Jul
29
revised Problem in showing that a sequence is a Cauchy sequence on a space with the integral metric.
edited body
Jul
29
answered the $C^\ast$-algebra $M_n(A)$, understanding the $C^\ast$-norm on $M_n(A)$
Jul
29
revised the $C^\ast$-algebra $M_n(A)$, understanding the $C^\ast$-norm on $M_n(A)$
added 4 characters in body; edited tags
Jul
29
revised composition and strong limits of completely positive maps is completely positive
edited tags
Jul
29
answered composition and strong limits of completely positive maps is completely positive
Jul
29
answered Why is $ab=ba=a^\ast b=ab^\ast=0$ (orthogonal elements in a $C^\ast$-algebra)?
Jul
29
revised Why is $ab=ba=a^\ast b=ab^\ast=0$ (orthogonal elements in a $C^\ast$-algebra)?
edited tags
Jul
29
answered Analytic version of Hahn-Banach using geometric version
Jul
29
answered On the existence of a particular type of real sequence of functions
Jul
29
comment Lang's treatment of product of Radon measures
I was talking about the context, not the theorem. When you defined Radon measure, you wrote property 3 for open sets. But in Lang's book he also includes $\sigma $-finite sets.
Jul
29
comment Properties of 1-Sphere in a linear normed space against a normed linear subspace.
Yes. Now, if you are not comfortable with sup, inf, and inequalities, you will have a hard time going on with functional analysis, since they are basic tools that are used a lot.
Jul
29
revised Properties of 1-Sphere in a linear normed space against a normed linear subspace.
added 1 character in body
Jul
29
revised Properties of 1-Sphere in a linear normed space against a normed linear subspace.
added 1 character in body
Jul
29
comment Properties of 1-Sphere in a linear normed space against a normed linear subspace.
It's just the very basic fact that in any set of real numbers with an infimum there is a sequence of elements of the set that converges to said infimum.
Jul
29
revised GNS construction and representations
edited tags
Jul
29
comment Closed subsets of Banach space
The sequence $(a_n,a_n') $ is in $Y $, but it is not Cauchy. It tells you nothing about the closedness of $Y $.
Jul
29
comment GNS construction and representations
No intuition necessary, this is very concrete: if $\|Tx\|\leq c\|x\|$ for all $x $, then $$\|Tx-Ty\|=\|T (x-y)\|\leq c\|x-y\|, $$ which tells you that given $\varepsilon >0$ for the definition of continuity, you can take $\delta=\varepsilon /c$.
Jul
29
comment Lang's treatment of product of Radon measures
I don't know how to do it in the current context. In any case, the context you provided is not exactly the one in Lang's book. Right now I don't have the time to follow the reasoning trail in Lang's book.
Jul
29
answered GNS construction and representations
Jul
29
revised GNS construction and representations
edited body