**Examples**

- The Hilbert-Schmidt operators on an infinite-dimensional Hilbert space form a Hilbert algebra with inner product (
*a*,*b*) = Tr (*b***a*). - If (
*X*, μ) is an infinite measure space, the algebra*L*∞ (*X*)*L*2(*X*) is a Hilbert algebra with the usual inner product from*L*2(*X*). - If
*M*is a von Neumann algebra with faithful semifinite trace τ, then the *-subalgebra*M*_{0}defined above is a Hilbert algebra with inner product (*a*,*b*) = τ(*b***a*). - If
*G*is a unimodular locally compact group, the convolution algebra*L*1(*G*)*L*2(*G*) is a Hilbert algebra with the usual inner product from*L*2(*G*). - If (
*G*,*K*) is a Gelfand pair, the convolution algebra*L*1(*K**G*/*K*)*L*2(*K**G*/*K*) is a Hilbert algebra with the usual inner product from*L*2(*G*); here*L**p*(*K**G*/*K*) denotes the closed subspace of*K*-biinvariant functions in*L**p*(*G*). - Any dense *-subalgebra of a Hilbert algebra is also a Hilbert algebra.

Read more about this topic: Commutation Theorem, Hilbert Algebras

### Other articles related to "examples":

Proverbs in Advertising

... Tatira has given a number of

... Tatira has given a number of

**examples**of proverbs used in advertising in Zimbabwe ... However, unlike the**examples**given above in English, all of which are anti-proverbs, Tatira's**examples**are standard proverbs ... above are meant to make a potential customer smile, in one of the Zimbabwean**examples**"both the content of the proverb and the fact that it is phrased as a proverb secure the idea of a secure time-h ...English Orthography - Spelling Irregularities - "Ough" Words

... though /oʊ/ as in toe (other

... though /oʊ/ as in toe (other

**examples**dough) tough /ʌf/ as in cuff (other**examples**rough, enough) cough /ɒf/ as in off (other**examples**Gough (name, some pronunciations)) hiccough (a now uncommon ...### Famous quotes containing the word examples:

“There are many *examples* of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”

—Bernard Mandeville (1670–1733)

“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied *examples* of his wrath.”

—G.C. (Georg Christoph)

“Histories are more full of *examples* of the fidelity of dogs than of friends.”

—Alexander Pope (1688–1744)

Main Site Subjects

Related Subjects

Related Phrases

Related Words