# Questions tagged [banach-algebras]

A Banach algebra is an algebra over the real or complex numbers which is equipped with a complete norm such that |xy| ≤ |x||y|. The study of Banach algebras is a major topic in functional analysis. If you are about to ask a question on C*-algebras or von Neumann algebras please use (c-star-algebras) or (von-neumann-algebras) instead (or in addition). Further related tags: (operator-algebras), (operator-theory), (banach-spaces), (hilbert-spaces).

1,217 questions
Filter by
Sorted by
Tagged with
29 views

### What is odd element of C*-algebra? [closed]

I cannot nowhere find a definition of an odd/even element of C*-algebra. Can someone write it here?
• 844
49 views

### Continuity of product in Banach Algebras

EDIT: The definition literally says that the product is bilinear, as Chris Eagle kindly pointed out. Turns out that my original proof was fine. This question does no longer require an answer and ...
• 300
66 views

• 1,384
44 views

### Understanding the proof of Fuglede's theorem

I am trying to understand this proof of Fuglede's theorem on wikipedia : Everything was making sense until the last sentence: "Considering the first-order terms in the expansion for small λ, we ...
• 2,973
30 views

### Banach space with continuous multiplication is a Banach algebra

Consider a Banach space $(\mathcal{A},\|\cdot\|_{\mathcal{A}}$) and assume that $\mathcal{A}$ is also an associative algebra with a unit element $I\in \mathcal{A}$ such that $\|I\|_{\mathcal{A}}=1$. ...
• 1,035
11 views

• 700
29 views

• 3,869
98 views

### Predual of disc algebra and $W(\mathbb{T})\neq A(\mathbb{D})$

I want prove that the Wiener algebra, $W(\mathbb{T})$, does not coincide with the disc algebra $A(\mathbb{D})$. I know that there are some ways to do this. For example, one smart way is use Rudin-...
• 1,384
66 views

• 336
41 views

### If $\Phi$ is injective, $X_1$ normal and Hausdorff and $X_2$ compact, then $F$ is surjective

Let $X_1,X_2$ be topological spaces and $F\in \mathcal{C}(X_2,X_1)$. Let $\Phi:\mathcal{C}_b(X_1,\mathbb{C})\to\mathcal{C}_b(X_2,\mathbb{C}): \Phi(f):=f\circ F$. Then $\Phi$ is a continuous ...
• 2,180
59 views

### ideals, projections and factors in VN algebras

I'm trying to solve some problems on Von Neumann algebra and I got the questions below. $Q1$. By definition we know a factor is a Von Neumann algebra with trivial center, i.e. a center consisting only ...
• 953
66 views

### Spectrum $\sigma(a)$ taken within the unitisation of a $C^*$-algebra

My question relates to reconciling the definition of the spectrum $\sigma(a)$ of a point $a$ in a $C^*$-algebra $A$ in both the unital case and the more general case using the unitisation, since I ...
• 2,530
1 vote
### Proving that if $C_0(X)$ is unital, then $X$ is compact
Apologies if this is simple, I'm having one of those days. Let $X$ be a locally compact Hausdorff space and $C_0(X)$ be the commutative $C^*$-algebra of continuous complex-valued functions on $X$ that ...