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Right Hilbert Algebra

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♭. Then A is a right Hilbert algebra if A has an inner product <·,·> satisfying:

1. For all xi in A, pi_r(xi):eta|->etaxi is bounded on A.

2. <xieta,zeta>=<xi,zetaeta^♭>.

3. The involution xi|->xi^♭ is closable.

4. The linear span A^2 of products xieta, xi,eta in A, is a dense subalgebra of A.

See also

Hilbert Algebra, Hilbert Space, Inner Product Space, Involutive Algebra, Left Hilbert Algebra, Linear Manifold, Modular Hilbert Algebra, Quasi-Hilbert Algebra, Ring, Subspace, Unimodular Hilbert Algebra, Vector Space, von Neumann Algebra

This entry contributed by Christopher Stover

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References

Nelson, B. "Tomita-Takesaki Theory." http://www.math.ucla.edu/~bnelson6/Tomita-Takesaki%20Theory.pdf.

Cite this as:

Stover, Christopher. "Right Hilbert Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RightHilbertAlgebra.html

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