Papers by Mohammad Moshtaghioun
Bulletin of The Iranian Mathematical Society, 2009
The purpose of this paper is to introduce and to dis- cuss the concept of p-approximation and p-o... more The purpose of this paper is to introduce and to dis- cuss the concept of p-approximation and p-orthogonality in vector spaces, and to obtain some results on p- orthogonality in vector spaces similar to some well known results on the orthogonality in normed spaces. We also discuss the concept of p-extension of linear functionals on a vector space, and give a characterization of linear functionals on a subspace having a unique p-extension Hahn-Banach to the whole vector space.
Bulletin of the Iranian Mathematical Society, Apr 1, 2014
For suitable Banach spaces X and Y with Schauder decompositions and a suitable closed subspace M ... more For suitable Banach spaces X and Y with Schauder decompositions and a suitable closed subspace M of some compact operator space from X to Y , it is shown that the strong Banach-Saks-ness of all evaluation operators on M is a sufficient condition for the weak Banach-Saks property of M, where for each x ∈ X and y * ∈ Y * , the evaluation operators on M are defined by ϕx(T) = T x and ψy * (T) = T * y * .
Abstract and Applied Analysis, 2012
By introducing the concept ofL-limited sets and thenL-limited Banach spaces, we obtain some chara... more By introducing the concept ofL-limited sets and thenL-limited Banach spaces, we obtain some characterizations of it with respect to some well-known geometric properties of Banach spaces, such as Grothendieck property, Gelfand-Phillips property, and reciprocal Dunford-Pettis property. Some complementability of operators on such Banach spaces are also investigated.
Journal of Mathematical Extension, Jun 29, 2018
Following the concept of L-limited sets in dual Banach spaces introduced by Salimi and Moshtaghio... more Following the concept of L-limited sets in dual Banach spaces introduced by Salimi and Moshtaghioun, we introduce the concept of almost L-limited sets in dual Banach lattices and then by a class of disjoint limited completely continuous operators on Banach lattices, we characterize Banach lattices in which almost L-limited subsets of their dual, coincide with L-limited sets.
International Journal of Analysis and Applications, 2018
We introduce and study the notion of limited p-Schur property (1 ≤ p ≤ ∞) of Banach spaces. Also,... more We introduce and study the notion of limited p-Schur property (1 ≤ p ≤ ∞) of Banach spaces. Also, we establish some necessary and sufficient conditions under which some operator spaces have the limited p-Schur property. In particular, we prove that if X and Y are two Banach spaces such that X contains no copy of 1 and Y has the limited p-Schur property, then K(X, Y) (the space of all compact operators from X into Y) has the limited p-Schur property.
Annals of Functional Analysis, 2018
We introduce the notion of the p-Schur property (1 ≤ p ≤ ∞) as a generalization of the Schur prop... more We introduce the notion of the p-Schur property (1 ≤ p ≤ ∞) as a generalization of the Schur property of Banach spaces, and then we present a number of basic properties and some examples. We also study its relation with some geometric properties of Banach spaces, such as the Gelfand-Phillips property. Moreover, we verify some necessary and sufficient conditions for the p-Schur property of some closed subspaces of operator spaces. = sup ∞ n=1 x n , x * p 1 p : x * ≤ 1 .
Taiwanese Journal of Mathematics, 2007
By introducing the concept of weakly completely continuous subspaces of operator ideals, it will ... more By introducing the concept of weakly completely continuous subspaces of operator ideals, it will be given some characterizations of this concept, specially in terms of relative weak compactness of all point evaluations related to that subspace. Also it is shown that the only Banach spaces such that all closed subspace of an operator ideal between them has this property, are reflexive Banach spaces.
Bulletin of the Korean Mathematical Society, 2010
For several Banach spaces X and Y and operator ideal U , if U (X, Y) denotes the component of ope... more For several Banach spaces X and Y and operator ideal U , if U (X, Y) denotes the component of operator ideal U ; according to Freedman's definitions, it is shown that a necessary and sufficient condition for a closed subspace M of U (X, Y) to have the alternative Dunford-Pettis property is that all evaluation operators φx : M → Y and ψ y * : M → X * are DP1 operators, where φx(T) = T x and ψ
Banach Journal of Mathematical Analysis, 2011
By introducing the concept of limited completely continuous operators between two arbitrary Banac... more By introducing the concept of limited completely continuous operators between two arbitrary Banach spaces X and Y , we give some properties of this concept related to some well known classes of operators and specially, related to the Gelfand-Phillips property of the space X or Y. Then some necessary and sufficient conditions for the Gelfand-Phillips property of closed subspace M of some operator spaces, with respect to limited complete continuity of some operators on M , so-called, evaluation operators, are verified.
IEEE Transactions on Signal Processing, 2014
We investigate the relationship between constant false alarm rate (CFAR) and invariant tests. We ... more We investigate the relationship between constant false alarm rate (CFAR) and invariant tests. We introduce the minimal invariant group (MIG). We show that for a family of distributions, the unknown parameters are eliminated from the distribution of the maximal invariant statistic under the MIG while the maximum information of the observed signal is preserved. We prove that any invariant test with respect to MIG is CFAR and conversely, for any CFAR test an invariant statistic exists with respect to an MIG under some mild conditions. Moreover for a given CFAR test, we propose a systematic method for deriving an enhanced test, i.e., a function of observations exists such that the likelihood ratio (LR) of the maximal invariant of its MIG gives an enhanced test. Furthermore, we introduce the uniformly most powerful-CFAR (UMP-CFAR) test as the optimal CFAR bound among all CFAR tests. We then prove that the UMP-CFAR test for the minimally invariant hypothesis testing problem is given by the LR of the maximal invariant under MIG. For some problems, this test (MP-CFAR) depends on the unknown parameters of the alternative hypothesis, however, provides an upper-performance bound for all suboptimal CFAR tests. We also propose three suboptimal novel CFAR tests among which one is asymptotically optimal.
Ukrainian Mathematical Journal, 2013
Introducing the concept of strong alternative Dunford-Pettis property (strong DP1) for the subspa... more Introducing the concept of strong alternative Dunford-Pettis property (strong DP1) for the subspace M of operator ideals U(X, Y) between Banach spaces X and Y, we show that M is a strong DP1 subspace if and only if all evaluation operators φx : M → Y and ψy * : M → X * are DP1 operators, where φx(T) = T x and ψy * (T) = T * y * for x ∈ X, y * ∈ Y * , and T ∈ M. Some consequences related to the concept of alternative Dunford-Pettis property in subspaces of some operator ideals are obtained. Введено поняття сильної альтернативної властивостi Данфорда-Петтiса (сильна DP1) для пiдпростору M операторних iдеалiв U(X, Y) мiж банаховими просторами X та Y, за допомогою якого показано, що M є сильним DP1 пiдпростором тодi i тiльки тодi, коли всi оператори оцiнки φx : M → Y та ψy * : M → X * є DP1 операторами, де φx(T) = T x та ψy * (T) = T * y * при x ∈ X, y * ∈ Y * та T ∈ M. Отримано деякi наслiдки щодо поняття альтернативної властивостi Данфорда-Петтiса в пiдпросторах деяких операторних iдеалiв.
By giving some necessary and sufficient conditions for the dual of operator subspaces to have the... more By giving some necessary and sufficient conditions for the dual of operator subspaces to have the Schur property, we improve the results of Brown,Ülger and Saksman-Tylli in the Banach space setting. In particular, under some conditions on Banach spaces X and Y , we show that for a subspace M of operator ideal U (X, Y), M * has the Schur property iff all point evaluations M1(x) = {T x : T ∈ M1} and f M1(y *) = {T * y * : T ∈ M1} are relatively norm compact, where x ∈ X, y * ∈ Y * and M1 is the closed unit ball of M.
Abstract and Applied Analysis, 2011
We give some new conditions for existence and uniqueness of best proximity point. We also introdu... more We give some new conditions for existence and uniqueness of best proximity point. We also introduce the concept of strongly proximity pair and give some interesting results.
Banach Journal of Mathematical Analysis, 2016
We introduce the concept of the strong Gelfand-Phillips (GP) property in Banach lattices, and we ... more We introduce the concept of the strong Gelfand-Phillips (GP) property in Banach lattices, and we characterize Banach lattices with the strong GP property. Next, by introducing the class of almost limited completely continuous operators from an arbitrary Banach lattice E to another F , we give some properties of them related to some well-known classes of operators and, especially, to the strong GP property of the Banach lattice E.
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Papers by Mohammad Moshtaghioun