4 edition of **Inverses of disjointness preserving operators** found in the catalog.

- 360 Want to read
- 26 Currently reading

Published
**2000**
by American Mathematical Society in Providence, R.I
.

Written in English

- Banach modules (Algebra),
- Operator theory.,
- Banach lattices.

**Edition Notes**

Statement | Y.A. Abramovich, A.K. Kitover. |

Series | Memoirs of the American Mathematical Society,, no. 679 |

Contributions | Kitover, A. K. |

Classifications | |
---|---|

LC Classifications | QA3 .A57 no. 679, QA326 .A57 no. 679 |

The Physical Object | |

Pagination | viii, 164 p. ; |

Number of Pages | 164 |

ID Numbers | |

Open Library | OL50258M |

ISBN 10 | 0821813978 |

LC Control Number | 99054530 |

Books and Monographs Banach C(K)-modules and operators preserving disjointness (with Y. Abramovich and E. Arenson), Pitman Research Notes in Mathematical Series #, Longman Scienti c & Technical, Inverses of Disjointness Preserving Operators (with Y. Abramovich), Memoirs of the Amer. Math. Soc. No, More editions of Inverses of Disjointness Preserving Operators (Memoirs of the American Mathematical Society): Inverses of Disjointness Preserving Operators (Memoirs of the American Mathematical Society): ISBN () .

A characterization of operators preserving disjointness in terms of their inverse. (English summary) Positivity and its applications (Ankara, ). Positivity 4 (), no. 3, – Recall that a linear operator T: X → Y between vector lattices is disjointness preserving if T sends disjoint elements from X to disjoint elements in Y. The characterization mentioned in the title is found. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.

Therefore, the above theorem tells us that all positive disjointness preserving operators between C() and C(S) are of composition multiplication type. The notion of disjointness elements has been extended to partially ordered vector spaces that are not necessarily Riesz spaces in [8]. Are positive disjointness preserving operators on subspaces of C. Inverses of Disjointness Preserving Operators (Memoirs of the American Mathematical Society) Dec 1, by Y. A. Abramovich, A. K. Kitover.

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Inverses of disjointness preserving operators Article (PDF Available) in Studia Mathematica (3) January with 90 Reads How we measure 'reads'. Inverses of disjointness preserving operators. [Yuri A Abramovich; Arkady K Kitover] Home. WorldCat Home About WorldCat Help.

Search. Search for Library Items Search for Lists Search for This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices.

Band preserving operators and band-projections 47 56; 8. Central operators and Problems A and B 57 66; 9. Range-domain exchange in the Huijsmans–de Pagter–Koldunov Theorem 72 81; d-splitting number of disjointness preserving operators 78 87; Essentially one-dimensional and discrete vector lattices 85 94; Inverses of disjointness preserving operators.

[Y A Abramovich; A K Kitover] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices.

PDF | A linear operator T: X --> Y between vector lattices is said to be disjointness preserving if T sends disjoint elements in X to disjoint elements | Find, read and cite all the research.

The inverse of band preserving and disjointness preserving operators by C.B. Huijsmans’ and A.W. Wickstead’ ’ Department of Mathematics, University of Leiden, P.O. BoxRA Leiden, the Netherlands ’ Department of Pure Mathematics, The Queen’s University of.

A.K. Kitover: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books.

COVID campus closures: see options for getting or retaining Remote Access to subscribed content. Positivity()– Positivity Disjointnesspreservingoperatorsonnormedpre-Riesz spaces:extensionsandinverses Anke.

The characterization mentioned in the title is found. Cite this article. Abramovich, Y., Kitover, A. A Characterization of Operators Preserving Disjointness in Terms of their Inverse. If ℝn is partially ordered by a generating closed cone K; then (ℝn;K) is a pre-Riesz space.

We show for a disjointness preserving bijection T on (ℝn;K) that the inverse of T is also disjointness preserving. We prove that for T there is k ∈ P(b) such that Tk is band preserving, where b is the number of bands in (ℝn;K); and P(b) the set of orders of permutations on b symbols.

Key words: Band, band preserving operator, disjointness preserving operator, d-isomor-phism, nite dimensional, generating closed cone, pre-Riesz space. Introduction. If X and Y are Banach lattices and T: X.

Y is a disjoint-ness preserving bijection, then in [8] and [9] it is shown that the inverse T1 is also disjointness preserving. Invertible disjointness preserving operators - Volume 37 Issue 1 - C. Huijsmans, B. De Pagter. invertible disjointness preserving operator from a uniformly complete vector lattice onto a normed vector lattice has a disjointness preserving inverse and is necessarily order bounded.

Local operators turn out to be a special class of disjointness preserving operators, whose definition we recall first. Definition Let X and Y be partially ordered vector spaces and let T: X → Y be a linear operator.

T is called disjointness preserving if for every x, y ∈ X from x ⊥ y in X it follows that T x ⊥ T y in Y. A linear operator T: X → Y between vector lattices is said to be disjointness preserving if T sends disjoint elements in X to disjoint elements in Y.

Two closely related questions are discussed in this paper: (1) If T is invertible, under what assumptions does the inverse operator also preserve disjointness.

Abramovich [HL] of whether the inverse of a one-to-one disjointness-preserving operator between Banach lattices is also disjointness preserving. The remaining part of the introduction contains some notation and termi-nology which will be needed in what follows.

If AT is a compact (always Hausdorff) topological space and / is a continuous. A linear operator T on a vector lattice L preserves disjointness if Tx ⊥ y whenever x ⊥ y. If such a T is positive it is automatically order bounded. An ortho-morphism is an order bounded disjointness preserving linear operator on L.

In this note we show that the theory of orthomorphisms on archimedean vector lattices admits a totally. The inverse of band preserving and disjointness preserving operators. By C.B. Huijsmans and A.W. Wickstead. Get PDF ( KB) Cite. BibTex; Full citation Publisher: Published by Elsevier B.V.

Year: DOI identifier: /(92) OAI identifier: Provided by. They leave open the questions of whether the inverse of a bijective disjointness-preserving operator between Dedekind complete vector lattices is disjointness-preserving (Problem 1 in this paper) and whether the inverse of any bijective bandpreserving operator on an Archimedean vector lattice is band-preserving (Problem 2 in this paper).

Disjointness preserving operators on normed pre-Riesz spaces: extensions and inverses. Positivity () doi: /s Kalauch, A.; Malinowski, H. Order continuous operators on pre-Riesz spaces and embeddings.

Anal. Anwend. 38(4) (). DISJOINTNESS PRESERVING OPERATORS An operator TE 2’(E) is called disjointness preserving if f I g implies Tf I Tg (f, ge E). If TE 2’(E) is disjointness preserving, then T is order bounded, that is T takes sets of the form {f~ E: g.a bounded linear operator on X, and ˙(T) be the spectrum of T.

˙ 1(T) = ˙(T) nf˘2C such that the set (˘I T)X is closed in X and either null(˘I T) of disjointness preserving operators. J 2 / Let us mention also Theorem~ that contains a description of such operators on arbitrary laterally complete vector lattices.

The central role in these descriptions is played by d-bases, one of two principal tools utilized in our work [{\it Inverses of Disjointness Preserving Operators}, Memoirs of the Amer. Math. Soc., forthcoming].