Annals of Functional Analysis最新文献

In this paper, we study the property of hereditary completeness of vector systems ({x_k}_{k=1}^infty) in a Hilbert space. A criterion of hereditary completeness is obtained in terms of projectors on closed linear spans of systems of the form ({x_k}_{k in N}), (N subset mathbb {N}). Developed technique has been used to prove that mixed systems of a hereditarily complete system are also hereditarily complete. In conclusion, the problem of possible defects in a nonhereditarily complete system is considered.

For (M_C=left( begin{array}{cccc}A& C 0& Bend{array}right)) acting on a Hilbert space ({mathcal{H}}oplus {mathcal{K}}), we first characterize the Fredholm completions with positive nullity and negative index. We then explore the weak approximate spectrum (sigma _{_textrm{Fa}}(M_C)) and the weak essential approximate spectrum (sigma _{_textrm{Fea}}(M_C)) of (M_C). In combination with the research, we give the equivalent conditions that make (M_C) have the weak property ((omega )) for any (Cin {mathcal{B}}({mathcal{K}},{mathcal{H}}).)

We characterize the primal, factorial, and Glimm ideals of the Haagerup tensor product (Votimes ^{h} B) of a TRO V and a (C^{*})-algebra B.

In this paper, we introduce a new class of function spaces, which unify and generalize Lorentz–Karamata spaces, variable Lorentz spaces, and other several classical function spaces. Based on the new spaces, we define five variable martingale Hardy–Lorentz–Karamata spaces and discuss the relationships among them. Our method is the atomic decomposition by some new techniques, which rigorously improves the known results in previous literature.

We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley–Wiener theorem for the linear canonical Dunkl transform. Further, we characterize the square-integrable function f whose linear canonical Dunkl transform of the function is supported in the polynomial domain. Finally, we develop the Boas-type Paley–Wiener theorem for the linear canonical Dunkl transform.

Consider the Dunkl Laplacian (Delta _k) associated with a root system (Phi) in (mathbb {R}^d) and a nonnegative multiplicity function k on (Phi). By following Stein (Proc Natl Acad Sci USA 73(7):2174–2175, 1976) and Strichartz (Trans Am Math Soc 148(2):461–471, 1970), we introduce and investigate a family of (Delta _k)-averaging operators parameterized by (alpha ge 0). This family includes the (Delta _k)-spherical and (Delta _k)-volume mean operators as special cases. We prove that, for each order (alpha ge 0), the averaging operator of order (alpha) satisfies a (Delta _k)-Pizzetti formula. In addition, we establish that this family of the (alpha)-averaging operators provides various mean value characterizations of harmonic, polyharmonic, subharmonic and metaharmonic functions in the Dunkl setting. Furthermore, some of these characterizations yield new mean value properties for the usual classes of such functions associated with the standard Laplace operator.

This paper aims to explore the Schatten properties of time–frequency localization operators with Lorentz symbols. Specifically, we determine the precise range of ((p,q,r)in [1,infty ]^3) such that for any (Fin L^{q,r}({{{{mathbb {R}}}}^{2d}})) (the Lorentz space with exponents (q, r)), the localization operator (mathcal {A}_F) belongs to (mathcal {S}_p(L^2({{{{mathbb {R}}}}^{2d}}))) (the Schatten class of order p).

Let (({mathcal {X}},d,mu )) be a space of homogeneous type with the upper dimension (omega). In this work, the authors characterize the sets of all pointwise multipliers of inhomogeneous Besov spaces (B_{p,q}^{s}( {mathcal {X}} )) and inhomogeneous Triebel–Lizorkin spaces (F_{p,q}^{s}({mathcal {X}})). When (pin [1,infty ]) and (s>frac{omega }{p}), the authors show that the set of all pointwise multipliers of (B_{p,q}^{s}({mathcal {X}})) equals to (B_{p,q,text {unif}}^{s}({mathcal {X}})) for (qin [p,infty )) or (M_{p,q}^{s}({mathcal {X}})) for (qin (0,p)) if and only if ({mathcal {X}}) supports the local lower and upper bound. Corresponding results for (F_{p,q}^{s}({mathcal {X}})) with (p,qin (1,infty )) and (s>frac{omega }{p}) are also obtained. When (ple 1) (or (p=infty)), the authors establish a characterization of the collection of all pointwise multipliers of (B_{p,p}^{s}({mathcal {X}})) [or (B_{infty ,q}^{s}({mathcal {X}}))], which does not need any extra assumption on (mu) and is even new when ({mathcal {X}}) supports the Ahlfors regular condition.

In this paper, we investigate the Davis-Wielandt shell and the numerical range of composition operators on the Hardy space. Firstly, we give a characterization of the Davis-Wielandt shell for multiplication operators with matrix symbols. Subsequently, we characterize the Davis-Wielandt shell of composition operators induced by constant functions, inner functions fixing 0 and elliptic automorphisms of order 2. Furthermore, we analyze the symmetry of the Davis-Wielandt shell for composition operators induced by parabolic automorphisms or elliptic automorphisms. Additionally, we present a complete description of the numerical range for composition operators induced by elliptic automorphisms of order 3.

We establish a boundary condition on the variable exponent p, for which the operators (U_z:fmapsto (fcirc varphi _z)varphi '_z) are bounded in (A^{p(cdot )}(textbf{D})). This boundary condition enables us to investigate the boundedness and compactness of Toeplitz operators (T_varphi) with symbols (varphi) in (L^1(textbf{D})), via the functions (zmapsto Vert U_zT_varphi U_z(mathbbm {1})Vert _{L^{p(cdot )}(textbf{D})}) and (zmapsto Vert U_zT_{overline{varphi }}U_z(mathbbm {1})Vert _{L^{p(cdot )}(textbf{D})}).