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Hilbert space (Definition)
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"Hilbert space" is owned by mathcam. [ full author list (2) | owner history (1) ]
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See Also: inner product space, Hilbert module, quadratic function associated with a linear functional, vector norm, Riesz sequence, von Neumann algebra, $L^2$-spaces are Hilbert spaces, quantum groups and von Neumann algebras, H * -algebra, Riesz-Fischer theorem, properties of orthogonal polynomials


Attachments:
example of non-separable Hilbert space (Example) by rspuzio
$L^2$-spaces are Hilbert spaces (Theorem) by asteroid
classification of Hilbert spaces (Theorem) by asteroid
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Cross-references: infinite dimensional, finite-dimensional, induce, inner product, norm, Banach space, metric, inner product space
There are 154 references to this entry.

This is version 8 of Hilbert space, born on 2002-02-13, modified 2004-12-07.
Object id is 1930, canonical name is HilbertSpace.
Accessed 19769 times total.

Classification:
AMS MSC46C05 (Functional analysis :: Inner product spaces and their generalizations, Hilbert spaces :: Hilbert and pre-Hilbert spaces: geometry and topology )

Pending Errata and Addenda
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Hilbert space always Banach space? by lha on 2003-10-01 03:39:29
Am I correct in thinking that a Hilbert space is always a Banach space? If so, could you say this explicitly? You can never have too many cross-references :)
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