scholarly journals Uniqueness of unconditional basis of $\ell _{2}\oplus \mathcal {T}^{(2)}$

2021 ◽  
pp. 1
Author(s):  
Fernando Albiac ◽  
José L. Ansorena
Keyword(s):  
Unconditional Basis

Projections on Tree-Like banach Spaces

1985 ◽  
Vol 37 (5) ◽  
pp. 908-920
Author(s):  
A. D. Andrew
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Unconditional Basis ◽  
Reflexive Banach Space ◽  
Separable Space ◽  
Bounded Linear ◽  
Tree Space

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.

Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean

Positivity ◽  
2010 ◽  
Vol 14 (4) ◽  
pp. 579-584 ◽  
Author(s):  
Fernando Albiac ◽  
Camino Leránoz
Keyword(s):  
Banach Spaces ◽  
Unconditional Basis

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

scholarly journals TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

2010 ◽  
Vol 88 (2) ◽  
pp. 205-230 ◽  
Author(s):  
CHRISTOPH KRIEGLER ◽  
CHRISTIAN LE MERDY
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Unconditional Basis ◽  
Compact Set ◽  
Bounded Operators ◽  
Space Setting ◽  
Uniformly Bounded

AbstractLet K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

scholarly journals James quasi reflexive space has the fixed point property

1989 ◽  
Vol 39 (1) ◽  
pp. 25-30 ◽  
Author(s):  
M.A. Khamsi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unconditional Basis ◽  
Fixed Point Property ◽  
Point Property ◽  
Reflexive Space ◽  
Lin's Method ◽  
Lin’S Method

We prove that the classical sequence James space has the fixed point property. This gives an example of Banach space with a non-unconditional basis where the Maurey-Lin's method applies.

scholarly journals Complex interpolation of a Banach space with its dual

2000 ◽  
Vol 87 (2) ◽  
pp. 200
Author(s):  
Frédérique Watbled
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Vector Space ◽  
Unconditional Basis ◽  
Scalar Product ◽  
Dual Space ◽  
Function Spaces ◽  
Complex Interpolation

Let $X$ be a Banach space compatible with its antidual $\overline{X^*}$, where $\overline{X^*}$ stands for the vector space $X^*$ where the multiplication by a scalar is replaced by the multiplication $\lambda \odot x^* = \overline{\lambda} x^*$. Let $H$ be a Hilbert space intermediate between $X$ and $\overline{X^*}$ with a scalar product compatible with the duality $(X,X^*)$, and such that $X \cap \overline{X^*}$ is dense in $H$. Let $F$ denote the closure of $X \cap \overline{X^*}$ in $\overline{X^*}$ and suppose $X \cap \overline{X^*}$ is dense in $X$. Let $K$ denote the natural map which sends $H$ into the dual of $X \cap F$ and for every Banach space $A$ which contains $X \cap F$ densely let $A'$ be the realization of the dual space of $A$ inside the dual of $X \cap F$. We show that if $\vert \langle K^{-1}a, K^{-1}b \rangle_H \vert \leq \parallel a \parallel_{X'} \parallel b \parallel_{F'}$ whenever $a$ and $b$ are both in $X' \cap F'$ then $(X, \overline{X^*})_{\frac12} = H$ with equality of norms. In particular this equality holds true if $X$ embeds in $H$ or $H$ embeds densely in $X$. As other particular cases we mention spaces $X$ with a $1$-unconditional basis and Köthe function spaces on $\Omega$ intermediate between $L^1(\Omega)$ and $L^\infty(\Omega)$.

scholarly journals The principles of the dependent and independent nationality of spouses: advantages and disadvantages

2018 ◽  
Vol 7 ◽  
pp. 105-121
Author(s):  
Seyyed Mohsen Hashemi-Nasab Zavareh ◽  
Elham Ghaffarian ◽  
Naser Ghamkhar
Keyword(s):  
Unconditional Basis ◽  
Present Situation ◽  
The Other ◽  
Main Question ◽  
Nationality Policy ◽  
Advantages And Disadvantages ◽  
The World

On marriage issues, many countries have espoused the independence of nationality policy, that is, they accept neutral effects of marriage on nationality. We don’t see the point of bestowing nationality on an alien woman who has married a national man but lives abroad. The ratio of countries in favor of dependent nationality to those in favor of independent nationality is one to three. So, there are only a few countries left still pursuing a policy of forcing husbands’ nationality upon alien women on an unconditional basis. The main question in this paper is: Should the nationality of one spouse be imposed on the other one, making them both subjects of one State? After an introduction (chapter Ⅰ), we analyze the theory of the unity of nationality and the theory of independent nationality (chapter Ⅱ). In chapter Ⅲ we see international documents on the theories of dependent and independent nationality. Finally, we take care of the present situation of the world in respect to nationality laws and then we resume some conclusions; the main one is that some political approaches seems to discriminates between national and foreign women.  

A Remark on Bases in Hardy Spaces

1984 ◽  
Vol 27 (3) ◽  
pp. 360-364
Author(s):  
Peter Sjögren
Keyword(s):  
Natural Number ◽  
Hardy Spaces ◽  
Unconditional Basis

AbstractThe Franklin spline system in [0,1] has been generalized by Strömberg to a system in ℝn which is an unconditional basis in Hp(ℝn) for p > n/(n + m +1). Here the natural number m is the order of the system. For some of these values of p, it was known that the Hp quasi-norm is equivalent to a certain expression containing the coefficients of the function with respect to this basis. We prove this equivalence for all p > n/(n + m +1).

Sign in / Sign up

Export Citation Format

Share Document