Spectral representations of operators in Hilbert spaces over quaternions and octonions

DOI10.1080/17476933.2010.538845zbMath1322.47029OpenAlexW2004120702MaRDI QIDQ3145029

Sergey V. Ludkovsky, Wolfgang Sprössig

Publication date: 13 December 2012

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2010.538845

zbMATH Keywords

quaternionsspectral representationoctonions

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Power-associative rings (17A05)

Related Items (10)

Structure of octonionic Hilbert spaces with applications in the Parseval equality and Cayley–Dickson algebras ⋮ Schauder bases in Dirac modules over quaternions ⋮ Category isomorphisms between Hilbert spaces over octonions and Hilbert spaces over Clifford algebras ⋮ Integral operators for nonlocally compact group modules ⋮ Unbounded normal operators in octonion Hilbert spaces and their spectra ⋮ Classification of left octonionic modules ⋮ On a class of right linearly differentiable functions of Cayley-Dickson variables ⋮ Completions and homomorphisms of infinite dimensional Cayley–Dickson algebras ⋮ Quasi-permutable normal operators in octonion Hilbert spaces and spectra ⋮ Para-linearity as the nonassociative counterpart of linearity

Cites Work

• Unnamed Item
• Spectral theory of super-differential operators of quaternion and octonion variables
• Differentiable functions of Cayley-Dickson numbers and line integration
• Algebras of operators in Banach spaces over the quaternion skew field and the octonion algebra
• Differentiable functions of quaternion variables.

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