40,748 reputation
32978
bio website uregina.ca/science/mathstat/…
location Regina, Canada
age 46
visits member for 2 years, 9 months
seen 1 hour ago

I'm an Operator Algebraist (which interestingly makes me an analyst!)


Sep
28
comment Follow up on a previous question of mine (characters in star algebra)
Of course it is not a C$^*$-algebra. The result is true in C$^*$-algebras, how could there be a counterexample? I'm addressing your question where you are considering a non-unital Banach algebra; you said that in such an algebra $\sigma (a) = \{ \tau (a) \mid \tau \in \Omega (A) \} \cup \{0\}$, which is what I wrote a counterexample to.
Sep
27
answered A question about functional calculus
Sep
27
comment Is this a matrix operator norm?
@alw: since you now know the answer, I suggest you post an answer yourself, showing that the max norm is an operator norm when the 1-norm is considered in the domain, and the infinity-norm in the codomain. You can also prove that it is not an operator norm with the definition you posted in the question, where you require the same norm in the domain and the codomain.
Sep
27
answered If $A$ is a $2\times 2$ matrix with a repeated eigenvalue $r$, then $\mathrm{e}^{At}=\mathrm{e}^{rt}\left[I+(A-rI)t\right]$
Sep
27
comment When Heine - Borel theorem holds
You are welcome.
Sep
27
answered When Heine - Borel theorem holds
Sep
26
comment Find the cartesian equation for $(e^t,t^2)$
Good point, thanks.
Sep
26
revised Find the cartesian equation for $(e^t,t^2)$
added 8 characters in body
Sep
26
answered Follow up on a previous question of mine (characters in star algebra)
Sep
25
answered Find the cartesian equation for $(e^t,t^2)$
Sep
25
revised Example of a function whose directional derivatives are always positive
edited tags
Sep
25
answered Example of a function whose directional derivatives are always positive
Sep
25
comment Follow up on a previous question of mine (characters in star algebra)
I'm not so sure about your characterization for the spectrum. How do you define $\sigma(a)$ for a non-unital algebra? Note that Martini's argument in the other question uses that the algebra is unital.
Sep
25
comment Bounded operators with infinite matrix representations
What would "its matrix representation" be? Such a thing is not canonical.
Sep
23
answered Polar decomposition in a finite von Neumann algebra
Sep
22
answered A question about positive forms on involutive algebras.
Sep
20
revised When two projections in a C*-algebra are “almost” Murray-von Neumann equivalent, they are equivalent
edited body
Sep
19
answered Trace of vectors
Sep
18
revised Prove that g is continuous.
edited tags
Sep
17
revised What is the difference between a point and a vector
edited body