1,989 research outputs found
Multipliers for p-Bessel sequences in Banach spaces
Multipliers have been recently introduced as operators for Bessel sequences
and frames in Hilbert spaces. These operators are defined by a fixed
multiplication pattern (the symbol) which is inserted between the analysis and
synthesis operators. In this paper, we will generalize the concept of Bessel
multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be
shown that bounded symbols lead to bounded operators. Symbols converging to
zero induce compact operators. Furthermore, we will give sufficient conditions
for multipliers to be nuclear operators. Finally, we will show the continuous
dependency of the multipliers on their parameters.Comment: 17 page
Perturbations of frames
In this paper, we give some sufficient conditions under which perturbations
preserve Hilbert frames and near-Riesz bases. Similar results are also extended
to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning
that some of our perturbation conditions are quite different from those used in
the previous literatures on this topic.Comment: to appear in Acta MAth. Sinica, English Serie
Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to
We prove that a Hilbert space frame \fti contains a Riesz basis if every
subfamily \ftj , J \subseteq I , is a frame for its closed span. Secondly we
give a new characterization of Banach spaces which do not have any subspace
isomorphic to . This result immediately leads to an improvement of a
recent theorem of Holub concerning frames consisting of a Riesz basis plus
finitely many elements
- …