Infinite Dimensional Analysis, Quantum Probability and Applications

PART I: Quantum Probability Methods.- The non-linear and quadratic quantization programs(Accardi et al.).- A pedagogical note on the computation of relative entropy of two n-mode gaussian states(Parthasarathy).- Quantum operators of the semicircle distributions(Popa et al.).- Quantum Probability for Modeling Cognition, Decision Making, and Artificial Intelligence(Khrennikov).- PART II: Quantum Information Methods.- Note on Complexity of Communication Processes (Watanabe).- Trace decreasing quantum dynamical maps: Divisibility and entanglement dynamics(Filippov).- Compound state, its conditionality and quantum mutual information(Matsuoka).- Block Markov Chains on Trees(Souissi).- PART III: Quantum Dynamical Systems.- Hilbert von Neumann Modules versus Concrete von Neumann Modules(Skeide).- Absorption and fixed points for semigroups of quantum channels(Girotti).- Characterization of Gaussian Quantum Markov Semigroups(Poletti).- A Mean-field Laser Quantum Master Equation(Fagnola et al.).- Unique ergodicity and weakly monotone Fock space(Crismale).- Part IV: Infinite Dimensional Analysis.- Solutions of infinite dimensional partial di erential equations(Draouil et al.).- On Some Properties of Solution Sets of Discontinuous Quantum Stochastic Di erential Inclusions(Dikko).-Fractional operators from vanishing Morrey to vanishing Campanato spaces in the variable exponent setting on quasi-metric measure spaces(Rafeiro et al.).- Part V: Operator Algebras.- Characterization of certain traces on von Neumann algebras(Bikchentaev).- Actions of -Morphisms on Certain Projections of C -Matrix Algebras(Shaheen).- Part VI: Stochastic Operators.- Compatible Linear Lypunov Function for Infinite Dimensional Volterra Quadratic Stochastic Operators(Embong).- Bijectivity of a Class of Lotka-Volterra