#### 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… Expand

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

- Mathematics
- 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… Expand

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… Expand

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

- Mathematics
- 2021

Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, State of Qatar; aydweik@qu.edu.qa Department of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar,… Expand

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… Expand

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

Krylov solvability of unbounded inverse linear problems

- Mathematics, Computer Science
- ArXiv
- 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. Expand

An Application of Infinite Sums and Products Relating to Spectral Synthesis

- Mathematics
- Missouri Journal of Mathematical Sciences
- 2019

#### References

SHOWING 1-10 OF 52 REFERENCES

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

Invariant subspace lattices of Lambert's weighted shifts

- Mathematics
- 1982

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 given… Expand

Invariant subspaces for algebras of subnormal operators. II

- Mathematics
- 1986

Every rationally cyclic subnormal operator has a hyperinvariant subspace. A bounded linear operator on a Hilbert space is defined to be subnormal if it is the restriction to an invariant subspace of… Expand

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… Expand

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… Expand