The invariant subspace problem

@article{Radjavi1982TheIS,
  title={The invariant subspace problem},
  author={Heydar Radjavi and Peter Rosenthal},
  journal={The Mathematical Intelligencer},
  year={1982},
  volume={4},
  pages={33-37}
}
Quasiaffinity and invariant subspaces
Special classes of intertwining transformations between Hilbert spaces are introduced and investigated, whose purposes are to provide partial answers to some classical questions on the existence ofExpand
El problema del subespacio invariante
El famoso problema del subespacio invariante lleva más de 80 años sin tener una respuesta completa. En este trabajo hacemos un breve recuento de algunos resultados que se han obtenido con laExpand
Lebesgue Measure on ℝ
TLDR
The goal of the next two chapters is to develop a new form of integration that, while not perfect, overcomes many of the innate flaws of the Riemann integral. Expand
Sequences and Series of Functions
Sequences and series of functions are natural extensions of the topics discussed in Chaps. 2 and 3 and many of their properties are derived in a straightforward manner from the results covered there.Expand
Sequences in ℝ
In this chapter we investigate the most basic concept of analysis, the limit of a sequence. The concepts of convergence and divergence will be the main focus of our discussion but we will also touchExpand
The Real Numbers
TLDR
To begin this study, the opening section provides a list of necessary preliminaries to develop a concrete foundation to support this intuitive understanding before progressing to a study of functions of a real variable. Expand
The Riemann Integral
Here we consider the familiar integral from calculus which is generally attributed to Riemann, though the idea of upper and lower sums for finding areas was used previously by Cauchy; otherExpand
Invariant subspaces for operators whose polynomials satisfy the (G1)-condition
Abstract In this note, we show that if T ∈ B ( H ) is such that p ( T ) satisfies the ( G 1 ) -condition for every polynomial p and if the outer boundary of the spectrum of T is a finite union ofExpand
The Levi-Civita equation, vector modules and spectral synthesis
The purpose of this paper is to give a survey on some recent results concerning spectral analysis and spectral synthesis in the framework of vector modulesand in close connection with the Levi-CivitaExpand
Spectral Analysis and Spectral Synthesis
Spectral analysis and spectral synthesis deal with the description of translation invariant function spaces over locally compact Abelian groups. One considers the space Open image in new window ofExpand
...
1
2
...

References

SHOWING 1-10 OF 34 REFERENCES
An operator not satisfying Lomonosov's hypothesis
Abstract An example is presented of a Hilbert space operator such that no non-scalar operator that commutes with it commutes with a non-zero compact operator. This shows that Lomonosov's invariantExpand
Ten years in Hilbert space
This is a report on progress in the theory of single operators in the 1970's. It is based for the most part, but not exclusively, on ten problems in Hilbert space posed in 1970 [21]; it reports whichExpand
Some invariant subspaces for subnormal operators
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 specialExpand
A geometric equivalent of the invariant subspace problem
It is shown that every operator has an invariant subspace if and only if every pair of idempotents has a common invariant subspace. An idempotent on a Hilbert space is a bounded linear operator whoseExpand
...
1
2
3
4
...