On the mean ergodic theorem in bicomplex Banach modules

DOI10.1007/s00006-023-01262-2OpenAlexW4319004922WikidataQ122625810 ScholiaQ122625810MaRDI QIDQ2681256

Panagiotis N. Koumantos

Publication date: 7 February 2023

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-023-01262-2

zbMATH Keywords

mean ergodic theorembicomplex Banach modules

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Ergodic theory of linear operators (47A35) Ergodic theorems, spectral theory, Markov operators (37A30) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bicomplex weighted Hardy spaces and bicomplex \(C^*\)-algebras
• Bicomplex linear operators on bicomplex Hilbert spaces and Littlewood's subordination theorem
• Bicomplex quantum mechanics. II: The Hilbert space
• Ergodic theorems. With a supplement by Antoine Brunel
• Markov structures on Clifford algebras
• On quasi-number algebras
• On an algebraic generalization of the quantum mechanical formalism
• On hyperbolic quasinumbers and Chebyshev-like functions
• Order topology in Minkowski space and applications
• Brownian motion, martingales and Itô formula in Clifford analysis
• Some fundamental theorems of functional analysis with bicomplex and hyperbolic scalars
• Hyperbolic harmonic functions and hyperbolic Brownian motion
• Topological bicomplex modules
• Infinite dimensional bicomplex spectral decomposition theorem
• Bicomplex quantum mechanics. I: The generalized Schrödinger equation
• On linear functionals and Hahn-Banach theorems for hyperbolic and bicomplex modules
• On the mean ergodic theorem
• Postulates for general quantum mechanics
• Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
• Bicomplex Holomorphic Functions
• Ergodic Theorem in Quantum Mechanics
• One-Parameter Semigroups for Linear Evolution Equations
• Proof of the Ergodic Theorem
• Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
• Bicomplex holomorphic functional calculus
• Mean Ergodic Theorems in Quantum Mechanics
• Mean ergodic theorem in Banach spaces
• The Ergodic Theorem in Quantum Statistical Mechanics