- 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) L2(X) is a Hilbert algebra with the usual inner product from L2(X).
- If M is a von Neumann algebra with faithful semifinite trace τ, then the *-subalgebra M0 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 L1(G)L2(G) is a Hilbert algebra with the usual inner product from L2(G).
- If (G, K) is a Gelfand pair, the convolution algebra L1(KG/K)L2(KG/K) is a Hilbert algebra with the usual inner product from L2(G); here Lp(KG/K) denotes the closed subspace of K-biinvariant functions in Lp(G).
- Any dense *-subalgebra of a Hilbert algebra is also a Hilbert algebra.
Other articles related to "examples":
... 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 ...
... 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 (16701733)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold peoples attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
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“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (16881744)