On topological properties of components of the surjective hull of the ideal of quasi-p-nuclear operators

1989 ◽  
Vol 52 (2) ◽  
pp. 168-172
Author(s):  
Mar�a Jos� Rivera
Keyword(s):  
Topological Properties ◽  
Nuclear Operators ◽  
The Ideal

scholarly journals The ideal of Lipschitz classical p-compact operators and its injective hull

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Toufik Tiaiba ◽  
Dahmane Achour
Keyword(s):  
Banach Space ◽  
Compact Operator ◽  
Metric Space ◽  
Metric Spaces ◽  
Compact Operators ◽  
Operator Ideal ◽  
Linear Case ◽  
Injective Hull ◽  
Nuclear Operators ◽  
The Ideal

Abstract We introduce and investigate the injective hull of the strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical p-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi p-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical p-compact operators.

scholarly journals Generalized Differenceλ-Sequence Spaces Defined by Ideal Convergence and the Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
The Ideal

We introduced the ideal convergence of generalized difference sequence spaces combining an infinite matrix of complex numbers with respect toλ-sequences and the Musielak-Orlicz function overn-normed spaces. We also studied some topological properties and inclusion relations between these spaces.

scholarly journals Bounded approximation properties in terms of $C[0,1]$

2012 ◽  
Vol 110 (1) ◽  
pp. 45 ◽  
Author(s):  
Åsvald Lima ◽  
Vegard Lima ◽  
Eve Oja
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Approximation Property ◽  
Integral Operators ◽  
Operator Ideal ◽  
Approximation Properties ◽  
Finite Rank Operators ◽  
Nuclear Operators ◽  
The Ideal

Let $X$ be a Banach space and let $\mathcal I$ be the Banach operator ideal of integral operators. We prove that $X$ has the $\lambda$-bounded approximation property ($\lambda$-BAP) if and only if for every operator $T\in \mathcal I(X,C[0,1]^*)$ there exists a net $(S_\alpha)$ of finite-rank operators on $X$ such that $S_\alpha\to I_X$ pointwise and 26767 \limsup_\alpha\|TS_\alpha\|_{\mathcal I}\leq\lambda\|T\|_{\mathcal I}. 26767 We also prove that replacing $\mathcal I$ by the ideal $\mathcal N$ of nuclear operators yields a condition which is equivalent to the weak $\lambda$-BAP.

scholarly journals Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Awad A. Bakery ◽  
Elsayed Abdelbayen Elnour Mohamed ◽  
Mohamed Alamin Ahmed
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relation ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
De La Vallée Poussin ◽  
Difference Sequence Spaces ◽  
The Ideal

In the present paper we introduced the ideal convergence of generalized difference sequence spaces combining de La Vallée-Poussin mean and Musielak-Orlicz function overn-normed spaces. We also study some topological properties and inclusion relation between these spaces.

scholarly journals The Ideal Convergence of Strongly of  Γ2inp-Metric Spaces Defined by Modulus

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
N. Subramanian ◽  
K. Balasubramanian ◽  
K. Chandrasekhara Rao
Keyword(s):  
Metric Spaces ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Ideal Convergence ◽  
The Ideal

The aim of this paper is to introduce and study a new concept of theΓ2space via ideal convergence defined by modulus and also some topological properties of the resulting sequence spaces were examined.

More on closed non-vanishing ideals in CB(X)

2020 ◽  
Vol 70 (4) ◽  
pp. 909-916
Author(s):  
Amin Khademi
Keyword(s):  
Supremum Norm ◽  
Topological Properties ◽  
Normed Algebra ◽  
Completely Regular ◽  
Vanishing Ideal ◽  
Algebraic Properties ◽  
Sequential Compactness ◽  
Countable Compactness ◽  
Vanishing Ideals ◽  
The Ideal

AbstractLet X be a completely regular topological space. For each closed non-vanishing ideal H of CB(X), the normed algebra of all bounded continuous scalar-valued mappings on X equipped with pointwise addition and multiplication and the supremum norm, we study its spectrum, denoted by 𝔰𝔭(H). We make a correspondence between algebraic properties of H and topological properties of 𝔰𝔭(H). This continues some previous studies, in which topological properties of 𝔰𝔭(H) such as the Lindelöf property, paracompactness, σ-compactness and countable compactness have been made into correspondence with algebraic properties of H. We study here other compactness properties of 𝔰𝔭(H) such as weak paracompactness, sequential compactness and pseudocompactness. We also study the ideal isomorphisms between two non-vanishing closed ideals of CB(X).

scholarly journals A generalization of the m-topology on C(X) finer than the m-topology

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2509-2515
Author(s):  
F. Azarpanah ◽  
F. Manshoor ◽  
R. Mohamadian
Keyword(s):  
Topological Properties ◽  
Compact Sets ◽  
Empty Interior ◽  
Topological Ring ◽  
Locally Compact ◽  
Regular Elements ◽  
Zero Function ◽  
The Ideal

It is well known that the component of the zero function in C(X) with the m-topology is the ideal C?(X). Given any ideal I ? C?(X), we are going to define a topology on C(X) namely the mI-topology, finer than the m-topology in which the component of 0 is exactly the ideal I and C(X) with this topology becomes a topological ring. We show that compact sets in C(X) with the mI-topology have empty interior if and only if X n T Z[I] is infinite. We also show that nonzero ideals are never compact, the ideal I may be locally compact in C(X) with the mI-topology and every Lindel?f ideal in this space is contained in C?(X). Finally, we give some relations between topological properties of the spaces X and Cm(X). For instance, we show that the set of units is dense in Cm(X) if and only if X is strongly zero-dimensional and we characterize the space X for which the set r(X) of regular elements of C(X) is dense in Cm(X).

scholarly journals A note concerning the ideal of nuclear operators

1996 ◽  
Vol 38 (2) ◽  
pp. 233-236
Author(s):  
Bruce A. Barnes
Keyword(s):  
Banach Algebra ◽  
Linear Operators ◽  
Nuclear Operator ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Nuclear Operators ◽  
Finite Dimensional ◽  
Dimensional Range ◽  
The Ideal

AbstractLet be a Banach algebra of bounded linear operators such that contains every operator with finite dimensional range. Then contains every nuclear operator.

Maximal d-Ideals in a Riesz Space

1983 ◽  
Vol 35 (6) ◽  
pp. 1010-1029 ◽  
Author(s):  
Charles B. Huijsmans ◽  
Ben de Pagter
Keyword(s):  
Riesz Space ◽  
Weak Order ◽  
Prime Ideals ◽  
Topological Properties ◽  
Order Unit ◽  
Structure Space ◽  
Maximal Ideals ◽  
Minimal Prime ◽  
The Ideal

We recall that the ideal I in an Archimedean Riesz space L is called a d-ideal whenever it follows from ƒ ∊ I that {ƒ}dd ⊂ I. Several authors (see [4], [5], [6], [12], [13], [15] and [18]) have considered the class of all d-ideals in L, but the set ℐd of all maximal d-ideals in L has not been studied in detail in the literature. In [12] and [13] the present authors paid some attention to certain aspects of the theory of maximal d-ideals, however neglecting the fact thatℐd, equipped with its hull-kernel topology, is a structure space of the underlying Riesz space L.The main purpose of the present paper is to investigate the topological properties of ℐd and to compare ℐd to other structure spaces of L, such as the space of minimal prime ideals and the space of all e-maximal ideals in L (where e > 0 is a weak order unit).

scholarly journals The Ideal of σ-Nuclear Operators and Its Associated Tensor Norm

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1192
Author(s):  
Ju Myung Kim ◽  
Keun Young Lee
Keyword(s):  
Nuclear Operators ◽  
Tensor Norm ◽  
The Ideal

We introduce a new tensor norm ( σ -tensor norm) and show that it is associated with the ideal of σ -nuclear operators. In this paper, we investigate the ideal of σ -nuclear operators and the σ -tensor norm.

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