PlanetMath: representations of Banach *-algebras are continuous

(more info)

Math for the people, by the people.

donor list - find out how

Main Menu

representations of Banach *-algebras are continuous

(Theorem)

Theorem - Let $\pi : \mathcal{A} \longrightarrow \mathcal{B}(H)$ be a representation of a Banach *-algebra $\mathcal{A}$ on a Hilbert space $H$ . Then $\pi$ is bounded and $\| \pi \| \leq 1$ .

"representations of Banach *-algebras are continuous" is owned by asteroid.

(view preamble | get metadata)

This object's parent.

Log in to rate this entry.
(view current ratings)

Cross-references: Hilbert space, Banach *-algebra, theorem

This is version 2 of representations of Banach *-algebras are continuous, born on 2007-08-09, modified 2007-08-09.
Object id is 9844, canonical name is RepresentationsOfBanachAlgebrasAreContinuous.
Accessed 591 times total.

Classification:

46K10 (Functional analysis :: Topological algebras with an involution :: Representations of topological algebras with involution)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact