Tagged Questions
4
votes
1answer
129 views
Fourier transform as a Gelfand transform
One question came to my mind while looking at the proof of Gelfand-Naimark theorem. Is Fourier transform a kind of Gelfand transform? Are there any other well-known transforms which are so?
1
vote
1answer
70 views
Continuity of Translation of the Trigonometric Polynomials
Had a question from Katznelson recorded in my journal which is still bugging me; I believe I have solved the following exercise subject to a minor point: Let $B$ be a Banach spach on $\mathbb{T}$ with ...
7
votes
2answers
164 views
Does the Banach algebra $L^1(\mathbb{R})$ have zero divisors?
Assume that the functions $f,g: \mathbb{R}\rightarrow \mathbb{R}$ are integrable and equal to zero on $(-\infty,0)$, (i.e $f,g \in L^+$). Then by Titchmarsh's theorem:
$f*g$ is zero almost everywhere ...
5
votes
3answers
521 views
Is $L^2(\mathbb{R})$ with convolution a Banach Algebra?
Is $L^2(\mathbb{R})$ a Banach algebra, with convolution?
I am pretty sure the answer is no, because I think that
$f,g \in L^2(\mathbb{R})$ does not imply that $f*g \in L^2(\mathbb{R})$. However, I ...
