THE SCHUR TEST OF COMPACT OPERATORS

Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).

COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK

In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and unitary.As a consequence,we characterize conjugations of the form A_(u,v).In addition,a class of conjugations of the form C_(λ,a)is introduced.We show that the class of conjugations C_(λ,a)coincides with the class of conjugations A_(u,v);we then characterize the complex symmetry of the Toeplitz operators T_(φ)with respect to the conjugation C_(λ,a).

BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT

In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H^(2)(D) and the Fock space g^(2).The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.

WEIGHTED COMPOSITION OPERATORS ON THE HILBERT SPACE OF DIRICHLET SERIES

In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.

Composition operators on weighted Bergman spaces induced by doubling weights

Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.

Dynamic Individual Selection and Crossover Boosted Forensic-based Investigation Algorithm for Global Optimization and Feature Selection

The advent of Big Data has rendered Machine Learning tasks more intricate as they frequently involve higher-dimensional data.Feature Selection(FS)methods can abate the complexity of the data and enhance the accuracy,generalizability,and interpretability of models.Meta-heuristic algorithms are often utilized for FS tasks due to their low requirements and efficient performance.This paper introduces an augmented Forensic-Based Investigation algorithm(DCFBI)that incorporates a Dynamic Individual Selection(DIS)and crisscross(CC)mechanism to improve the pursuit phase of the FBI.Moreover,a binary version of DCFBI(BDCFBI)is applied to FS.Experiments conducted on IEEE CEC 2017 with other metaheuristics demonstrate that DCFBI surpasses them in search capability.The influence of different mechanisms on the original FBI is analyzed on benchmark functions,while its scalability is verified by comparing it with the original FBI on benchmarks with varied dimensions.BDCFBI is then applied to 18 real datasets from the UCI machine learning database and the Wieslaw dataset to select near-optimal features,which are then compared with six renowned binary metaheuristics.The results show that BDCFBI can be more competitive than similar methods and acquire a subset of features with superior classification accuracy.

半平面函数空间上复合算子的差分

本文刻画半平面Korenblum空间上复合算子差分的有界性、紧性和序有界性,并探究复合算子差分的相应性质在半平面Bergman空间与Korenblum空间之间的差异性.

Weighted composition operators on the Fock space

In this paper,we study weighted composition operators on theFock space F^(2).We prove that each bounded composition operator on F^(2) is complex symmetric.This is in sharp contrast with the phenomenon on the Hardy space H^(2)(D).We characterize Hermitian weighted composition operators and algebraic weighted composition operators with degree less than or equal to two on F^(2).In addition,we investigate cyclicity and hypercyclicity of complex symmetric weighted composition operators.We also characterize those weighted compositionoperators that preserveframes,tight frames or normalized tight frames on F^(2).Finally,we study mean ergodicity and uniformly mean ergodicity of weighted composition operators.

Multi-strategies Boosted Mutative Crow Search Algorithm for Global Tasks:Cases of Continuous and Discrete Optimization

Crow Search Algorithm(CSA)is a swarm-based single-objective optimizer proposed in recent years,which tried to inspire the behavior of crows that hide foods in different locations and retrieve them when needed.The original version of the CSA has simple parameters and moderate performance.However,it often tends to converge slowly or get stuck in a locally optimal region due to a missed harmonizing strategy during the exploitation and exploration phases.Therefore,strategies of mutation and crisscross are combined into CSA(CCMSCSA)in this paper to improve the performance and provide an efficient optimizer for various optimization problems.To verify the superiority of CCMSCSA,a set of comparisons has been performed reasonably with some well-established metaheuristics and advanced metaheuristics on 15 benchmark functions.The experimental results expose and verify that the proposed CCMSCSA has meaningfully improved the convergence speed and the ability to jump out of the local optimum.In addition,the scalability of CCMSCSA is analyzed,and the algorithm is applied to several engineering problems in a constrained space and feature selection problems.Experimental results show that the scalability of CCMSCSA has been significantly improved and can find better solutions than its competitors when dealing with combinatorial optimization problems.The proposed CCMSCSA performs well in almost all experimental results.Therefore,we hope the researchers can see it as an effective method for solving constrained and unconstrained optimization problems.

Difference of composition operators over the half-plane

To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the halfplane for all index choices.For applications,we obtain direct analytic characterizations of the bounded and compact differences of composition operators on such spaces.This paper concludes with a joint Carleson measure characterization when the difference of composition operators is Hilbert-Schmidt.

Cauchy变换型空间上复合算子的线性组合

本文研究从Cauchy变换型空间到Korenblum空间上复合算子线性组合的紧性问题.本文证明该线性组合的紧性与其在加权Bergman空间上的紧性是等价的.