عنوان

Decomposability and triangularizability of positive operators on Banach lattices

Number

TLpq304380235

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Decomposability and triangularizability of positive operators on Banach lattices

General Material Designation

[Thesis]

First Statement of Responsibility

M. T. Jahandideh

Subsequent Statement of Responsibility

H. Radjavi

Name of Publisher, Distributor, etc.

Dalhousie University (Canada)

Date of Publication, Distribution, etc.

1997

Specific Material Designation and Extent of Item

108

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

Dalhousie University (Canada)

Text preceding or following the note

1997

Text of Note

The main results in this thesis are about invariant subspaces of multiplicative semigroups of quasinilpotent positive operators on Banach lattices. There are some known results that guarantee the existence of a non-trivial closed invariant ideal for a quasinilpotent positive operator on certain spaces, for example on usdC\sb0(\Omega)usd with usd\Omegausd a locally compact Hausdorff space or on a Banach lattice with atoms. Some recent results also guarantee the existence of non-trivial closed invariant ideals for a compact quasinilpotent positive operator on an arbitrary Banach lattice. In fact it is known that given such an operator T, on a real or complex Banach lattice, there is a nontrivial closed ideal which is invariant under all positive operators that commute with T. This thesis deals with invariant ideals for families of positive operators on Banach lattices. In particular it studies ideal-decomposable and ideal-triangularizable semi-groups of positive operators. We show that in certain Banach lattices compactness is not required for the existence of hyperinvariant closed ideals for a quasinilpotent positive operator. We also show that in those Banach lattices a semigroup of quasinilpotent positive operators might be decomposable without imposing any compactness condition. We generalize the fact that the only irreducible usdC\sb{p}usd-closed subalgebra of usdC\sb{p}usd is usdC\sb{p}usd itself to extend some recent reducibility results and apply them to derive some decomposability theorems concerning a collection of quasinilpotent positive operators on reflexive Banach lattices. We use these results for "ideal-triangularization", i.e., we construct a maximal closed ideal chain, each of whose members is invariant under a certain collection of operators that are related to compact positive operators, or to quasinilpotent positive operators.

Mathematics

Pure sciences

H. Radjavi

M. T. Jahandideh

Electronic name

p

[Thesis]

276903

a

Y