Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces

Othman Echi

Displaying similar documents to “Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces”

Fine and quasi connectedness in nonlinear potential theory

David R. Adams, John L. Lewis (1985)

Annales de l'institut Fourier

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If $B_{α, p}$ denotes the Bessel capacity of subsets of Euclidean $n$ -space, $α > 0$ , $1 < p < \infty$ , naturally associated with the space of Bessel potentials of $L^{p}$ -functions, then our principal result is the estimate: for $1 < α p \leq n$ , there is a constant $C = C (α, p, n)$ such that for any set $E$ $min {B_{α, p} (E \cap Q), B_{α, p} (E^{c} \cap Q)} \leq C \cdot B_{α, p} (Q \cap \partial_{f} E)$ for all open cubes $Q$ in $n$ -space. Here $\partial_{f} E$ is the boundary of the $E$ in the $(α, p)$ -fine topology i.e. the smallest topology on $c$ -space that makes the associated $(α, p)$ -linear potentials continuous there. As a consequence,...

Topological characterizations of ordered groups with quasi-divisor theory

Jiří Močkoř (2002)

Czechoslovak Mathematical Journal

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For an order embedding $G \overset{h}{\to} \to Γ$ of a partly ordered group $G$ into an $l$ -group $Γ$ a topology $𝒯_{\hat{W}}$ is introduced on $Γ$ which is defined by a family of valuations $W$ on $G$ . Some density properties of sets $h (G)$ , $h (X_{t})$ and $(h (X_{t}) ∖ {h (g_{1}), \dots, h (g_{n})})$ ( $X_{t}$ being $t$ -ideals in $G$ ) in the topological space $(Γ, 𝒯_{\hat{W}})$ are then investigated, each of them being equivalent to the statement that $h$ is a strong theory of quasi-divisors.

Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel&#039;yanov, Manfred P. H. Wolff (2001)

Studia Mathematica

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Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace $X ₀ : = x \in X : l i m_{n \to \infty} | | T ⁿ x | | = 0$ is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness $χ_{| | \cdot | | ₁} (A) < 1$ for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove...

Quasi-algebraic representability of sets in $R^{n}$ .

W. Waliszewski (1984)

Banach Center Publications

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Inclusion Indices of Quasi-Banach Spaces

Fernando Cobos, Luz M. Fernández-Cabrera, Antonio Manzano, Antón Martínez (2007)

Bollettino dell'Unione Matematica Italiana

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We investigate inclusion indices for quasi-Banach spaces. First we consider the case of function spaces on $[0,1]$ , then the sequence case and finally we develop an abstract approach dealing with indices defined by the real interpolation scale gen- erated by a quasi-Banach couple.

The quasi Isbell topology on function spaces

D. N. Georgiou, A. C. Megaritis (2015)

Colloquium Mathematicae

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In this paper, on the family (Y) of all open subsets of a space Y we define the so called quasi Scott topology, denoted by $τ_{q S c}$ . This topology defines in a standard way, on the set C(Y,Z) of all continuous maps of the space Y to a space Z, a topology $t_{q I s}$ called the quasi Isbell topology. The latter topology is always larger than or equal to the Isbell topology, and smaller than or equal to the strong Isbell topology. Results and problems concerning the topology $t_{q I s}$ are given.

On quasi-compactness of operator nets on Banach spaces

Eduard Yu. Emel'yanov (2011)

Studia Mathematica

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The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net ${(T_{λ})}_{λ}$ is equivalent to quasi-compactness of some operator $T_{λ}$ . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.

Relationship of certain rings of infinite matrices over integers

Mario Petrich, Pedro V. Silva (2000)

Bollettino dell'Unione Matematica Italiana

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Sia $N$ l'insieme degli interi non negativi e $Z$ l'anello degli interi. Sia $A$ l'anello delle matrici $N \times N$ su $Z$ che hanno solo un numero finito di cifre non nulle in ogni linea ed in ogni colonna. Sia $B$ il sottoanello generato da $X$ e $Y$ , dove $X$ (rispettivamente $Y$ ) è ottenuto dalla matrice identità muovendo gli 1 una posizione a destra (rispettivamente in giù). Sia pure $C$ il sottoanello di $A$ generato da $1 - X$ e $1 - Y$ . Infine sia $F$ il sottoanello delle matrici di $A$ che hanno solo un numero finito di cifre...

Some remarks on quasi-Cohen sets

Pascal Lefèvre, Daniel Li (2001)

Colloquium Mathematicae

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We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection $C (G) / C_{E^{c}} (G) ↪ L ²_{E} (G)$ is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.

Quasi-greedy bases and Lebesgue-type inequalities

S. J. Dilworth, M. Soto-Bajo, V. N. Temlyakov (2012)

Studia Mathematica

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We study Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy bases. We mostly concentrate on the $L_{p}$ spaces. The novelty of the paper is in obtaining better Lebesgue-type inequalities under extra assumptions on a quasi-greedy basis than known Lebesgue-type inequalities for quasi-greedy bases. We consider uniformly bounded quasi-greedy bases of $L_{p}$ , 1 < p < ∞, and prove that for such bases an extra multiplier in the Lebesgue-type inequality can be taken...