Banach in a sentence

Banach spaces General Banach spaces are more complicated than Hilbert spaces, and cannot be classified in such a simple manner as those.

Bounded linear operators over Banach space form a Banach algebra in respect to the standard operator norm.

Comparing this with the example for Banach spaces, we see that the Banach space direct sum and the Hilbert space direct sum are not necessarily the same.

Conversely, the Lindenstrauss–Tzafriri theorem asserts that if every closed subspace of a Banach space is complemented, then the Banach space is isomorphic (topologically) to a Hilbert space.

In the same article, Kwapień proved that the validity of a Banach-valued Parseval's theorem for the Fourier transform characterizes Banach spaces isomorphic to Hilbert spaces.

The Banach–Steinhaus theorem is not limited to Banach spaces.

Therefore, a Banach space cannot be the union of countably many closed subspaces, unless it is already equal to one of them; a Banach space with a countable Hamel basis is finite-dimensional.

The Stone–Weierstrass theorem mentioned above, for example, relies on Banach algebras which are both Banach spaces and algebras.

The theory of real Banach algebras can be very different from the theory of complex Banach algebras.

When the Banach algebra A is the algebra L(X) of bounded linear operators on a complex Banach space X (e.

In Encampment, Susan Munson and Stas Banach were the top two vote-getters.

District III Legislator Dan Banach, also a member of the Penn Yan Municipal Utilities Board, said the village is looking for help to pay for the $2 million cost of installing the equipment.

I called Edo Banach, the president of the National Hospice and Palliative Care Organization, to get the trade group’s response.

A Banach space can be canonically identified with a subspace of its bidual, which is the dual of its dual space.

A Banach space isomorphic to all its infinite-dimensional closed subspaces is isomorphic to a separable Hilbert space.

A free group on a two-element set S occurs in the proof of the Banach–Tarski paradox and is described there.

After Banach solved some mathematics problems which Steinhaus considered difficult, they published their first joint work.

After the Red Army recaptured Lviv in the Lvov–Sandomierz Offensive of 1944, Banach returned to the University and helped re-establish it after the war years.

Also, the notion of derivative can be extended to arbitrary functions between Banach spaces.

An important object of study in functional analysis are the continuous linear operators defined on Banach and Hilbert spaces.