Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Compact-like operators in lattice-normed spaces
Download
index.pdf
Date
2017
Author
Aydın, Abdullah
Metadata
Show full item record
Item Usage Stats
193
views
144
downloads
Cite This
Let $(X,p,E)$ and $(Y,m,F)$ be two lattice-normed spaces. A linear operator $T:Xto Y$ is said to be $p$-compact if, for any $p$-bounded net $x_alpha$ in X, the net $Tx_alpha$ has a $p$-convergent subnet in Y. That is, if $x_alpha$ is a net in X such that there is a $ein E_+$ satisfying $p(x_alpha) ≤ e$ for all $alpha$, then there exists a subnet $x_{alpha_beta}$ and $y_in Y$ such that $m(Tx_{alpha_beta} −y) xrightarrow{o}0$ in $F$. A linear operator $T:Xto Y$ is called $p$-continuous if $p(x_alpha) xrightarrow{o}0$ in $E$ implies $m(Tx_alpha) xrightarrow{o}$ in $F$, where $x_alpha$ is a net in $X$. $p$-compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, $AM$-compact operators, etc. Also, $p$-continuous operators generalize many classes of operators such as order continuous, norm con- tinuous, Dunford-Pettis, etc. Similar to $M$-weakly and $L$-weakly compact operators, we define $p$-$M$-weakly and $p$-$L$-weakly compact operators and study some of their properties. We also study up-continuous and up-compact operators between lattice- normed vector lattices. We give some results about acting mixed-normed spaces on lattice normed spaces.
Subject Keywords
Compact operators.
,
Vector analysis.
,
Lattice theory.
URI
http://etd.lib.metu.edu.tr/upload/12620945/index.pdf
https://hdl.handle.net/11511/26427
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Compact-like operators in lattice-nonmed. spaces
AYDIN, ABDULLAH; Emelyanov, Eduard; ERKURŞUN ÖZCAN, NAZİFE; Marabeh, M. A. A. (2018-04-01)
A linear operator T between two lattice-normed spaces is said to be p-compact if, for any p-bounded net x(alpha),,the net Tx(alpha) has a p-convergent subnet. p-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, AM-compact operators, etc. Similar to M-weakly and L-weakly compact operatois, we define p-M-weakly and p-L-weakly compact operators and study some of their properties. We also study up-continuous and up"compact operators between la...
Commuting Nilpotent Operators and Maximal Rank
Öztürk, Semra (Springer Science and Business Media LLC, 2010-01-01)
Let X, (X) over tilde be commuting nilpotent matrices over k with nilpotency p(t), where k is an algebraically closed field of positive characteristic p. We show that if X - (X) over tilde is a certain linear combination of products of pairwise commuting nilpotent matrices, then X is of maximal rank if and only if (X) over tilde is of maximal rank.
Quasi constricted linear representations of abelian semigroups on Banach spaces
Emelyanov, Eduard (2002-07-24)
Let (X, ∥·∥) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup IP in L(X), i.e. representations (Tt)t∈IP which satisfy the following conditions: i) limt→∞ ∥Ttx∥ < ∞ for all x ∈ X. ii) X0:= {x ∈ X:limt→∞ ∥Ttx∥ = 0} is closed and has finite codimension. We show that an asymptotically bounded representation (Tt)t∈IP is quasi constricted if and only if it has an attractor A with Hausdorff measure of noncompactness X∥·∥1 (A) < 1 with respect to some equi...
RELATIVE GROUP COHOMOLOGY AND THE ORBIT CATEGORY
Pamuk, Semra (2014-07-03)
Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups HG with rkHrkG-1. We answer this question negatively by calculating the relative group cohomology FH*(G, ?(2)) where G = Z/2xZ/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology FH*(G, M) can be calc...
Characterization of Riesz Spaces with Topologically Full Center
Alpay, Safak; Orhon, Mehmet (2013-07-26)
Let E be a Riesz space and let E-similar to denote its order dual. The orthomorphisms Orth(E) on E, and the ideal center Z(E) of E, are naturally embedded in Orth(E-similar to) and Z(E-similar to) respectively. We construct two unital algebra and order- continuous Riesz homomorphisms.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
A. Aydın, “Compact-like operators in lattice-normed spaces,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.