bibkey: vidalcadavidrodriguez2020hilbert
authors: Sebastian J. Vidal; Paula Cadavid; Pablo M. Rodriguez
year: 2020
title: "Hilbert evolution algebras and its connection with discrete-time Markov chains"
doi: 10.48550/arXiv.2012.05124
url: https://arxiv.org/abs/2012.05124v2
claim: "Definition 2.2 gives the real-or-complex Hilbert evolution algebra framework with complete natural orthonormal bases and bounded left multiplication."
strata_touched:
  - D5/S3/QuadraticForms/EvolutionAlgebras/HilbertNaturalBasisNonuniqueness
license: citation-only
triage: anchor

Hilbert evolution algebras

Definition 2.2 uses a real or complex separable Hilbert space, a bilinear multiplication, and a complete orthonormal natural basis. For every fixed vector v, left multiplication satisfies a bound $\Vert vw\Vert \le M_v\Vert w\Vert$ for some $M_v>0$ and every w. The preceding discussion uses convergent Hilbert expansions, not Hamel bases. Corollary 2.4 supplies the Hilbert realization framework for a uniformly bounded square table. These ingredients do not assert uniqueness of natural orthonormal bases when the square is dense.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2012.05124
• URL: https://arxiv.org/abs/2012.05124v2
• Text: https://arxiv.org/html/2012.05124v2
• Locations: the Schauder-basis and product discussion preceding Definition 2.2; Definition 2.2; Corollary 2.4.