Additive functionals and operators on a quaternionic Hilbert space

DOI10.1063/1.528454zbMath0664.46080OpenAlexW2038854630MaRDI QIDQ3814251

D. F. Almeida, Chandra Shekhar Sharma

Publication date: 1989

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528454

zbMATH Keywords

algebra of additive operatorsmultiplication by scalar for functionalsRiesz representation theorem for quaternionic Hilbert spacesstructure of functionals and operators on a quaternionic Hilbert space

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Applications of operator algebras to the sciences (47L90) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Abstract operator algebras on Hilbert spaces (47L30) Miscellaneous applications of functional analysis (46N99)

Related Items (7)

Coherent states and Hermite polynomials on quaternionic Hilbert spaces ⋮ Some Peculiarities of Quaternionic Linear Spaces ⋮ Additive isometries on a quaternionic Hilbert space ⋮ General construction of reproducing kernels on a quaternionic Hilbert space ⋮ S-spectrum and associated continuous frames on quaternionic Hilbert spaces ⋮ On interactions of quaternionic and complex structures of linear spaces ⋮ A direct proof of Wigner's theorem on maps which preserve transition probabilities between pure states of quantum systems

Cites Work

• Quaternion quantum mechanics: Second quantization and gauge fields
• Calculus on complex Banach spaces
• Quaternionic quantum field theory
• Spectral theory for unitary operators on a quaternionic Hilbert space
• The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem
• Semilinear operators
• The KS-transformation in hypercomplex form
• Quaternions in Relativity

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