scholarly journals HYPONORMAL OPERATORS, WEIGHTED SHIFTS AND WEAK FORMS OF SUPERCYCLICITY

2006 ◽  
Vol 49 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Frédéric Bayart ◽  
Etienne Matheron
Keyword(s):  
Banach Space ◽  
Unitary Operator ◽  
Dimensional Subspace ◽  
The Other ◽  
Hyponormal Operator ◽  
Weighted Shifts ◽  
One Dimensional ◽  
Other Hand ◽  
Hyponormal Operators

AbstractAn operator $T$ on a Banach space $X$ is said to be weakly supercyclic (respectively $N$-supercyclic) if there exists a one-dimensional (respectively $N$-dimensional) subspace of $X$ whose orbit under $T$ is weakly dense (respectively norm dense) in $X$. We show that a weakly supercyclic hyponormal operator is necessarily a multiple of a unitary operator, and we give an example of a weakly supercyclic unitary operator. On the other hand, we show that hyponormal operators are never $N$-supercyclic. Finally, we characterize $N$-supercyclic weighted shifts.

scholarly journals AN OPERATOR SUMMABILITY OF SEQUENCES IN BANACH SPACES

2013 ◽  
Vol 56 (2) ◽  
pp. 427-437 ◽  
Author(s):  
ANIL KUMAR KARN ◽  
DEBA PRASAD SINHA
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Borel Measure ◽  
Operator Ideal ◽  
The Other ◽  
Summable Sequence ◽  
Other Hand ◽  
Limited Operator

AbstractLet 1 ≤ p < ∞. A sequence 〈 xn 〉 in a Banach space X is defined to be p-operator summable if for each 〈 fn 〉 ∈ lw*p(X*) we have 〈〈 fn(xk)〉k〉n ∈ lsp(lp). Every norm p-summable sequence in a Banach space is operator p-summable whereas in its turn every operator p-summable sequence is weakly p-summable. An operator T ∈ B(X, Y) is said to be p-limited if for every 〈 xn 〉 ∈ lpw(X), 〈 Txn 〉 is operator p-summable. The set of all p-limited operators forms a normed operator ideal. It is shown that every weakly p-summable sequence in X is operator p-summable if and only if every operator T ∈ B(X, lp) is p-absolutely summing. On the other hand, every operator p-summable sequence in X is norm p-summable if and only if every p-limited operator in B(lp', X) is absolutely p-summing. Moreover, this is the case if and only if X is a subspace of Lp(μ) for some Borel measure μ.

scholarly journals Feller chains and random functions

2015 ◽  
Vol 56 ◽  
Author(s):  
Vytautas Kazakevičius
Keyword(s):  
Random Function ◽  
Transition Probability ◽  
The Other ◽  
One Dimensional ◽  
Random Functions ◽  
Other Hand ◽  
Dimensional Distribution ◽  
The One

We prove that each Feller transition probability is the one-dimensional distribution of some stochastically continuous random function. We also introduce the notion of a regular random function and show, on one hand, that every random  function has a regular modification, and on the other hand, that the composition of independent regular stochastically continuous random functions is stochastically continuous as well.

Two-dimensional partial orderings: Undecidability

1980 ◽  
Vol 45 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Alfred B. Manaster ◽  
Joseph G. Rosenstein
Keyword(s):  
Bipartite Graph ◽  
Bipartite Graphs ◽  
The Other ◽  
Two Dimensional ◽  
One Dimensional ◽  
Recursive Model ◽  
Linear Orderings ◽  
Other Hand ◽  
Partial Orderings ◽  
Planar Lattices

In this paper we examine the class of two-dimensional partial orderings from the perspective of undecidability. We shall see that from this perspective the class of 2dpo's is more similar to the class of all partial orderings than to its one-dimensional subclass, the class of all linear orderings. More specifically, we shall describe an argument which lends itself to proofs of the following four results:(A) the theory of 2dpo's is undecidable:(B) the theory of 2dpo's is recursively inseparable from the set of sentences refutable in some finite 2dpo;(C) there is a sentence which is true in some 2dpo but which has no recursive model;(D) the theory of planar lattices is undecidable.It is known that the theory of linear orderings is decidable (Lauchli and Leonard [4]). On the other hand, the theories of partial orderings and lattices were shown to be undecidable by Tarski [14], and that each of these theories is recursively inseparable from its finitely refutable statements was shown by Taitslin [13]. Thus, the complexity of the theories of partial orderings and lattices is, by (A), (B) and (D), already reflected in the 2dpo's and planar lattices.As pointed out by J. Schmerl, bipartite graphs can be coded into 2dpo's, so that (A) and (B) could also be obtained by applying a Rabin-Scott style argument [9] to Rogers' result [11] that the theory of bipartite graphs is undecidable and to Lavrov's result [5] that the theory of bipartite graphs is recursively inseparable from the set of sentences refutable in some finite bipartite graph. (However, (C) and (D) do not seem to follow from this type of argument.)

Some Random Fixed Point Theorems and Comparing Random Operator Equations

2011 ◽  
Vol 52-54 ◽  
pp. 127-132
Author(s):  
Ning Chen ◽  
Bao Dan Tian ◽  
Ji Qian Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
The Other ◽  
Operator Equations ◽  
Random Solution ◽  
Random Fixed Point ◽  
Other Hand ◽  
The Common

In this paper, some new results are given for the common random solution for a class of random operator equations which generalize several results in [4], [5] and [6] in Banach space. On the other hand, Altman’s inequality is also extending into the type of the determinant form. And comparing some solution for several examples, main results are theorem 2.3, theorem 3.3-3.4, theorem 4.1 and theorem 4.3.

scholarly journals On the Bishop-Phelps-Bollobás Property for Numerical Radius

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Sun Kwang Kim ◽  
Han Ju Lee ◽  
Miguel Martín
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Sufficient Conditions ◽  
The Other ◽  
Numerical Radius ◽  
Infinite Dimensional ◽  
Other Hand ◽  
Nikodym Property

We study the Bishop-Phelps-Bollobás property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces to ensure the BPBp-nu. Among other results, we show thatL1μ-spaces have this property for every measureμ. On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-nu. In particular, this shows that the Radon-Nikodým property (even reflexivity) is not enough to get BPBp-nu.

Numerical Simulation of AlxGa1-XN/GaN Hetero Junction Quantum Well by AMPS-1D

2011 ◽  
Vol 282-283 ◽  
pp. 518-521
Author(s):  
Kai Ju Zhang ◽  
B. Wan
Keyword(s):  
Numerical Simulation ◽  
Quantum Well ◽  
The Other ◽  
Simulation Program ◽  
One Dimensional ◽  
Photonic Structures ◽  
Other Hand ◽  
Dimensional Simulation ◽  
The One

In this work, the one dimensional simulation program called analysis of microelectronic and photonic structures (AMPS-1D) is used to study the performances of depth of AlxGa1-xN/GaN heterojunction quantum well. The calculated results of AMPS-1D software show that the effect of different Al composition on the depth of AlxGa1-xN/GaN heterojunction quantum well is slight. On the other hand, the effect of different doped concentration in AlxGa1-xN is obvious.

On order structure and operators in L ∞(μ)

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Irina Krasikova ◽  
Miguel Martín ◽  
Javier Merí ◽  
Vladimir Mykhaylyuk ◽  
Mikhail Popov
Keyword(s):  
Banach Space ◽  
Compact Operator ◽  
Linear Functional ◽  
Continuous Operator ◽  
The Other ◽  
Order Structure ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Other Hand ◽  
Continuous Operators

AbstractIt is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.

scholarly journals Spaces of vector functions that are integrable with respect to vector measures

2007 ◽  
Vol 82 (1) ◽  
pp. 85-109 ◽  
Author(s):  
José Rodríguez
Keyword(s):  
Banach Space ◽  
Probability Space ◽  
Equivalence Classes ◽  
The Other ◽  
Normed Spaces ◽  
Vector Measures ◽  
Other Hand ◽  
Integrable Functions ◽  
Compact Range ◽  
Indefinite Integral

AbstractWe study the normed spaces of (equivalence classes of) Banach space-valued functions that are Dobrakov,S* or McShane integrable with respect to a Banach space-valued measure, where the norm is the natural one given by the total semivariation of the indefinite integral. We show that simple functions are dense in these spaces. As a consequence we characterize when the corresponding indefinite integrals have norm relatively compact range. On the other hand, we also determine when these spaces are ultrabornological. Our results apply to conclude, for instance, that the spaces of Birkhoff (respectively McShane) integrable functions defined on a complete (respectively quasi-Radon) probability space, endowed with the Pettis norm, are ultrabornological.

scholarly journals A Banach Space which is not Equivalent to an Adjoint Space

1958 ◽  
Vol 11 (2) ◽  
pp. 105-105
Author(s):  
J. D. Weston
Keyword(s):  
Banach Space ◽  
The Other ◽  
Other Hand ◽  
Elementary Argument ◽  
Elementary Fact ◽  
Adjoint Space

A Banach space which is not reflexive may or may not be equivalent (in Banach's sense) to an adjoint space. For example, it is an elementary fact that the space (l), though not reflexive, is equivalent to (co)*, where (co) is the space of all sequences that converge to zero, normea in the usual way. On the other hand, (co) itself is not equivalent to any adjoint space : this can be proved by means of the Krein-Milman theorem, but here we obtain the result by an elementary argument which is scarcely more complicated than the standard proof that (co) is not reflexive.

scholarly journals Analytic vectors in continuousp-adic representations

2009 ◽  
Vol 145 (1) ◽  
pp. 247-270 ◽  
Author(s):  
Tobias Schmidt
Keyword(s):  
Banach Space ◽  
Lie Group ◽  
The Other ◽  
Induced Representations ◽  
Faithful Functor ◽  
Other Hand ◽  
Derived Functors

AbstractGiven a compactp-adic Lie groupGover a finite unramified extensionL/ℚplet GL/ℚpbe the product over all Galois conjugates ofG. We construct an exact and faithful functor from admissibleG-Banach space representations to admissible locallyL-analyticGL/ℚp-representations that coincides with passage to analytic vectors in the caseL=ℚp. On the other hand, we study the functor ‘passage to analytic vectors’ and its derived functors over general basefields. As an application we compute the higher analytic vectors in certain locally analytic induced representations.

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