عنوان

Decomposability and triangularizability of positive operators on Banach lattices

شماره

TLpq304380235

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Decomposability and triangularizability of positive operators on Banach lattices

نام عام مواد

[Thesis]

نام نخستين پديدآور

M. T. Jahandideh

نام ساير پديدآوران

H. Radjavi

نام ناشر، پخش کننده و غيره

Dalhousie University (Canada)

تاریخ نشرو بخش و غیره

1997

نام خاص و کميت اثر

108

جزئيات پايان نامه و نوع درجه آن

Ph.D.

کسي که مدرک را اعطا کرده

Dalhousie University (Canada)

امتياز متن

1997

متن يادداشت

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.

موضوع مستند نشده

Mathematics

موضوع مستند نشده

Pure sciences

مستند نام اشخاص تاييد نشده

H. Radjavi

مستند نام اشخاص تاييد نشده

M. T. Jahandideh

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y