Frame-cyclic operators and their properties
| Autor: | Mohammad Janfada, Nastaran Alizadeh Moghaddam |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Class (set theory) Pure mathematics Applied Mathematics Frame (networking) Statistical and Nonlinear Physics 01 natural sciences Unitary state 010305 fluids & plasmas Operator (computer programming) Mathematics::K-Theory and Homology 0103 physical sciences Orbit (control theory) 010301 acoustics Mathematical Physics Separable hilbert space Mathematics |
| Zdroj: | Infinite Dimensional Analysis, Quantum Probability and Related Topics. 24:2150009 |
| ISSN: | 1793-6306 0219-0257 |
| DOI: | 10.1142/s0219025721500090 |
| Popis: | Motivated by frame-vector for a unitary system, we study a class of cyclic operators on a separable Hilbert space which is called frame-cyclic operators. The orbit of such an operator on some vector, namely frame-cyclic vector, is a frame. Some properties of these operators on finite- and infinite-dimensional Hilbert spaces and their relations with cyclic and hypercyclic operators are established. A lower and upper bound for the norm of a self-adjoint frame-cyclic operator is obtained. Also, construction of the set of frame-cyclic vectors is considered. Finally, we deal with Kato’s approximation of frame-cyclic operators and discuss their frame-cyclic properties. |
| Databáze: | OpenAIRE |
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