Invariant Subspaces of Abstract Multiplication Operators

Invariant subspaces of abstract multiplication operators

INVARIANT SUBSPACES OF ABSTRACT MULTIPLICATION OPERATORS by Hermann Flaschka We describe a class of operators on a Banach space ft whose members behave, in a sense, like multiplication operators, and consequently leave invariant a proper closed subspace of IB. One of the sufficient conditions for an operator to be such an "abstract multiplication" bears a striking resemblence to an assumption m...

Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant sub-spaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.

Doubly Invariant Subspaces of Annulus Operators

Selfadjoint time operators and invariant subspaces

For classical dynamical systems time operators are introduced as selfadjoint operators satisfying the so called weak Weyl relation (WWR) with the unitary groups of time evolution. Dynamical systems with time operators are intrinsically irreversible because they admit Lyapounov operators as functions of the time operator. For quantum systems selfadjoint time operators are defined in the same way...

Internal time operators and invariant subspaces

An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage (MPC) based on a non-unitary similarity transformation Λ mapping reversible dynamics into irreversible ones. In a previous work a characterization of the irreversible dynamics induced by the MPC theory, the structure of the reversible evolutions admitting such type of change of representation and a prototype for th...