The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive, and uniformly expansive. Additionally, equivalent conditions for these concepts are provided in the case that the system is dissipative.
In this paper we characterize Li-Yorke chaotic composition operators on Orlicz spaces. Indeed some necessary and suffcient conditions are provided for Li-Yorke chaotic composition operator C' on the Orlicz space Lp. In some cases we have equivalent conditions for composition operators on Orlicz spaces to be Li-Yorke chaotic. The results of this paper extend similar results in Lp-spaces. Our results are essentially based on the results of [4].
In this paper, we investige the concept of expansivity for composition operators on Orlicz-Lorentz spaces. We study necessary and sufficient conditions for expansivity, positive expansivity and uniformly expansivity for composition operators $C_τ$ on $\mathbb{L}^{φ,h}(μ)$. We extend the of results of [15] into Orlicz-Lorentz spaces
In this paper, we study the Li-Yorke chaotic composition operators on Orlicz-Lorentz space. In fact, necessary and sufficient conditions are given for Li-Yorke chaotic composition operator $C_τ$ on $\mathbb{L}^{φ,h}(μ)$. Further, we present the equivalent conditions for $C_τ$ to be Li-Yorke chaotic. This paper's results are the generalization of results of [15] into Orlicz-Lorentz spaces.
Multiplication and composition operators between two Orlicz spaces
本文考虑复合算子$C_φ generated by nonsingular measurable transformation $ T $ and multiplication operator $ M_u $ generated by measurable function $ u $ between two different Orlicz spaces, then we investigate boundedness, compactness and essential norm of multiplication and composition operators in term of properties of the mapping $ φ $, the function $ u $ and the measure space $（X，X，μ）$.
Boundedness of composition operator in Orlicz-Morrey spaces
Graduate School of Information Science and Technology, The University of Osaka（大阪大学大学院信息科学技术研究科）；Center for Advanced Intelligence Project RIKEN（理化学研究所先进智能项目中心）；Center for Science Adventure and Collaborative Research Advancement (SACRA), Graduate School of Science, Kyoto University（京都大学理学研究院科学冒险与合作研究推进中心）；Center for Mathematics and Data Science, Gunma University（群马大学数学与数据科学中心）
The kernel of composition operator $C_T$ on Orlicz-Sobolev space is obtained. Using the kernel, a necessary and a sufficient condition for injectivity of composition operator $C_T$ has been established. Composition operators on Orlicz-Sobolev space with finite ascent as well as infinite ascent have been characterized.
We describe the Lorentz space $L(p, r), 0 < r < p, p > 1$, in terms of Orlicz type classes of functions L . As a consequence of this result it follows that Stein's characterization of the real functions on $R^n$ that are differentiable at almost all the points in $R^n$, is equivalent to the earlier characterization of those functions given by A. P. Calderon.
We show that the weighted Bergman-Orlicz space $A\_α^ψ$ coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function $ψ$ satisfies the so-called $Δ^{2}$--condition. In addition we prove that this condition characterizes those $A\_α^ψ$ on which every composition operator is bounded or order bounded into the Orlicz space $L\_α^ψ$. This provides us with estimates of the norm and the essential norm of composition operators on such spaces. We also prove that when $ψ$ satisfies the $Δ^{2}$--condition, a composition operator is compact on $A\_α^ψ$ if and only …
In this paper we deal with unbounded composition operators defined in Orlicz spaces. Indeed, we provide some necessary and sufficient condition for densely definedness of composition operators on Orlicz spaces. Also, we will investigate the adjoint of densely defined composition operators and we give some equivalent conditions for it to be densely defined. In addition, we show that densely defined composition operator is continuous if and only if it is everywhere defined. Finally, we characterize densely defined continuous composition operators.
A new class of convex functions called functions, Young functions, strong Young functions and Orlicz functions are introduced by relaxing the definitions of functions, Young functions, strong Young functions and Orlicz functions. Then, new classes of Orlicz spaces and Orlicz Sobolev space will be defined.
Let $Φ_1$ and $Φ_2$ be nondecreasing functions from $\mathbb{R_+}=(0,\infty)$ onto itself. For $i=1,2$ and $γ\in \mathbb{R}$, define the Orlicz class $L_{Φ_{i}}(\mathbb{R_+})$ to be the set of Lebesgue-measurable functions $f$ on $\mathbb{R_+}$ such that \begin{equation*} \int_{\mathbb{R_+}} Φ_{i} \left( k|(Tf)(t)| \right) t^γdt < \infty \end{equation*} for some $k>0$. Our goal in this paper is to find conditions on $Φ_1$, $Φ_2$, $γ$ and an operator $T$ so that the assertions \begin{equation} T : L_{Φ_2,t^γ}(\mathbb{R_+}) \rightarrow L_{Φ_1,t^γ}(\mathbb{R_+}), \tag{I} \end{equation} and \begin…
In this paper, the definition of noncommutative Orlicz sequence spaces is given, these spaces generalize the Schatten classes Sp(H). After some relations of trace and norm on this spaces have been researched, one give the criterion of reflexivity of these spaces. At last, as an application, we find the Toeplitz operator on the Bergman space belongs to some noncommutative Orlicz sequence spaces, hence the trace and the norm of operator could be computed.
Let $1\le p\le\infty$. A Banach lattice $X$ is said to be $p$-disjointly homogeneous or $(p-DH)$ (resp. restricted $(p-DH)$) if every normalized disjoint sequence in $X$ (resp. every normalized sequence of characteristic functions of disjoint subsets) contains a subsequence equivalent in $X$ to the unit vector basis of $\ell_p$. We revisit $DH$-properties of Orlicz spaces and refine some previous results of this topic, showing that $(p-DH)$-property is not stable in the class of Orlicz spaces and the classes of restricted $(p-DH)$ and $(p-DH)$ Orlicz spaces are different. Moreover, we give a c…
In this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of continuity in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $L^{p}$-spaces, $1\leq p<\infty $, and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming $f$ in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improve…
In this paper, we study spaceability of subsets of generalized Orlicz and Lebesgue spaces associated to Banach function space. Also, we give some sufficient conditions for spaceability of subsets of a general Banach space which improves an important result on this topic. As an application, it is shown that the set of all bounded linear operators which are not positive semidefinite on a separable Hilbert space is spaceable.
Given a fully symmetric Banach function space $E$ and a decreasing positive weight $w$ on $I = (0, a)$, $0 < a \le \infty $, the generalized Lorentz space $Λ_{E,w}$ is defined as the symmetrization of the canonical copy $E_w$ of $E$ on the measure space associated with the weight. If $E$ is an Orlicz space then $Λ_{E,w}$ is an Orlicz-Lorentz space. An investigation of the Köthe duality of these classes is developed that is parallel to preceding works on Orlicz-Lorentz spaces. First a class of functions $M_{E,w}$, which does not need to be even a linear space, is similarly defined as the symme…
