Singly generated invariant subspaces in the Hardy space on the unit ball | Zendy

Beyaz Başak Koca | Zendy; Nazım Sadık | Zendy

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Singly generated invariant subspaces in the Hardy space on the unit ball

Author(s) -

Beyaz Başak Koca,

Nazım Sadık

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1810-65

Subject(s) - linear subspace , hardy space , invariant (physics) , mathematics , invariant subspace , unit sphere , subspace topology , reflexive operator algebra , pure mathematics , combinatorics , mathematical analysis , computer science , mathematical physics , compact operator , extension (predicate logic) , programming language

In this paper, we give a complete characterization of singly generated invariant subspaces in the Hardy space on the unit ball. Then we construct a singly generated invariant subspace that cannot be generated by a single inner function, contrary to the one-variable case where every invariant subspace is generated by a single inner function. Some important properties of invariant subspaces are also determined for singly generated invariant subspaces.

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