## 10 Citations

On the Invariant Subspace Problem

- Mathematics
- 2016

In an attempt to solve the invariant subspace problem, we introduce a certain orthonormal basis of Hilbert spaces, and prove that a bounded linear operator on a Hilbert space must have an invariant…

The invariant subspaces of the shift plus integer multiple of the Volterra operator on Hardy spaces

- MathematicsArchiv der Mathematik
- 2018

AbstractČučković and Paudyal recently characterized the lattice of invariant subspaces of the shift plus a complex Volterra operator on the Hilbert space $$H^2$$H2 on the unit disk. Motivated by the…

Krylov solvability of unbounded inverse linear problems

- MathematicsArXiv
- 2020

Intrinsic operator-theoretic mechanisms are identified that guarantee or prevent Krylov solvability, with new features arising due to the unboundedness, in the self-adjoint case.

Applications of fixed point theorems in the theory of invariant subspaces

- Mathematics
- 2012

We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant…

A novel procedure for constructing invariant subspaces of a set of matrices

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2022

A problem that is frequently encountered in a variety of mathematical contexts is to find the common invariant subspaces of a single or of a set of matrices. A new method is proposed that gives a…

Applications of fixed point theorems in the theory of invariant subspaces

- Mathematics
- 2012

*Correspondence: lacruz@us.es Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Avenida Reina Mercedes, Seville, 41012, Spain Abstract We survey several…

Some Banach algebra structures for l^p({\beta}) and their operators

- Mathematics
- 2013

In this paper we consider the generalized Duhamel product ~ on l^p({\beta}) and characterize some Banach algebra structures for l^p({\beta}).

Examples of Diagonal Operators That Fail Spectral Synthesis on Spaces of Analytic Functions

- Mathematics
- 2011

An Application of Infinite Sums and Products Relating to Spectral Synthesis

- MathematicsMissouri Journal of Mathematical Sciences
- 2019

## References

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Quasinilpotent Operators and the Invariant Subspace Problem

- Mathematics
- 1997

In this paper we construct quasinilpotent operators without nontrivial invariant subspaces. As well as being interesting in its own right, we believe that this is a sensible (perhaps necessary) first…

On a characterization of invariant subspace lattices of weighted shifts

- Mathematics
- 1982

The paper concems itself with the characterization of invariant subspace lattices of weighted shift operators on the Hilbert space 12 with suitable conditions on their weights. This characterization…

Some invariant subspaces for subnormal operators

- Mathematics
- 1978

A theorem of D.E. Sarason is used to show that all subnormal operators have nontrivial invariant subspaces if some very special subnormal operators have them. It is then shown that these special…

Shifts on Hilbert spaces.

- Mathematics
- 1961

Does every operator on an infinite-dimensional Hubert space have a non-trivial invariant subspace ? The question is still unanswered. A possible approach is to classify all invariant subspaces of all…

Some recent developments in operator theory

- Mathematics
- 1978

The spectral picture of an operator Pulling out direct summands The reducing essential matricial spectra of an operator Quasitriangular operators Spectral characterization of nonquasitriangular…

On two problems concerning linear transformations in hilbert space

- Mathematics
- 1949

T n "0 We shall denote by Cf and C$ the closed linear manifolds spanned by { f}o and {T*'g}o, respectively; f , g being elements in H. This study is devoted to two general problems concerning the…

INVARIANT SUBSPACES OF COMPLETELY CONTINOUS OPERATIONS

- Mathematics
- 1954

Abstract : A proof is presented of the theorem that if B is a Banach space and if T is a completely continuous operator in B, there then exist proper invariant subspaces of T. The proof assumes…

Invariant subspace lattices of Lambert's weighted shifts

- Mathematics
- 1982

Abstract Let B(H) be the Banach algebra of all (bounded linear) operators on an infinite-dimensional separable complex Hilbert space H and let be a bounded sequence of positive real numbers. For a…

Cyclic vectors of weighted shifts on ^{} spaces

- Mathematics
- 1980

Various authors have studied the existence of cyclic vectors of weighted shifts on Banach spaces (Hilbert spaces). In this paper, the existence of cyclic vectors of weighted shifts on IP Banach…

Non-standard analysis

- Mathematics
- 1966

* General Introduction * Tools from Logic * Differential and Integral Calculus * General Topology * Functions of a Real Variable * Functions of a Complex Variable * Linear Spaces * Topological Groups…