Annals of Functional Analysis最新文献

The aim of this note is to prove that, given two superreflexive Banach spaces X and Y, then (Xwidehat{otimes }_pi Y) is superreflexive if and only if either X or Y is finite-dimensional. In a similar way, we prove that (Xwidehat{otimes }_varepsilon Y) is superreflexive if and only if either X or Y is finite-dimensional.

Let (({mathcal {A}},G,alpha )) be a separable groupoid (C^*)-dynamical system and (C_0(G^{(0)},{mathcal {A}})) the (C^*)-algebra of continuous sections that vanish at infinity. When (({mathcal {A}},G,alpha )) has the approximation property, we prove that the crossed product ({mathcal {A}}rtimes _{alpha ,r}G) is exact if and only if (C_0(G^{(0)},{mathcal {A}})) is exact. In particular, if G is topologically amenable and (C_0(G^{(0)},{mathcal {A}})) is exact, then ({mathcal {A}}rtimes _{alpha ,r}G) is exact.

Let ({mathcal {H}}) be a complex Hilbert space of dimension at least 3 and (mathcal {B(H)}) the algebra of all bounded linear operators on ({mathcal {H}}). For any (A, Bin {mathcal {B}}({mathcal {H}})), A and B are said to be orthogonal if (A^*B=0). In this paper, we establish the general form of orthogonality preserving bijections on (mathcal {B(H)}). Furthermore, we obtain a characterization of bijections (varphi :mathcal {B(H)}rightarrow mathcal {B(H)}) satisfying (varphi (A)bot (varphi (B)-varphi (C))) if and only if (Abot (B-C)) for any (A,B,Cin mathcal {B(H)}).

In this short note, we obtain several inequalities for unitarily invariant norms which are generalizations of the results shown by Zou et al. [Linear Algebra Appl. 562 (2019) 154–162] and [J. Math. Inequal. 10 (2016) 1119–1122]. At the same time, we generalize a result by Audenaert [Oper. Matrices. 9 (2015) 475–479].

We introduce the concept of vector-valued holomorphic mappings on the complex unit disk that factor through a Hilbert space and state the main properties of the space formed by such Bloch mappings equipped with a natural norm: linearization, Bloch transposition, surjective and injective Banach ideal property, Kwapień-type characterization by Bloch domination, and duality.

Let (H^{2}(mathbb {D}^{2})) be the Hardy module over the bidisc, and (M^{2}_{psi ,phi }) the submodule generated by ((psi (z)-phi (w))^{2}), where (psi ) and (phi ) are two inner functions. Let (N^{2}_{psi ,phi }=H^2(mathbb {D}^2)ominus M^{2}_{psi ,phi }) be the corresponding quotient module. The submodules and quotient modules are important objects in multivariable operator theory; Wu and Yu have shown that (N^{2}_{psi ,phi }) is essential normal. In this paper, the core operator of the submodule (M^{2}_{psi ,phi }=[(psi (z)-phi (w))^{2}]) is proved to be Hilbert–Schmidt, and its norm is computed. Furthermore, the Hilbert–Schmidt norms of the commutators ([S_{z}^{*},S_{z}]), ([S_{z}^{*},S_{w}]) and ([S_{w}^{*},S_{w}]) on (N^{2}_{psi ,phi }) are given.

Let (Omega ) be a class of C*-algebras with the m-comparison property (respectively, the n-almost divisibility property, the weakly (k, n)-divisibility property). We show that any infinite-dimensional simple unital C*-algebra in the class GTA(Omega ) (the class of C*-algebras which can be generalized tracially approximated by the C*-algebras in (Omega )) has m-comparison (respectively, is ((2n+1))-almost divisible, is weakly (k, 2n)-divisible).

We construct a class of subspace lattices ({mathcal {L}}) on a separable infinite dimensional Hilbert space (mathcal {K}). Let ({{,textrm{Alg},}}{mathcal {L}}) be the corresponding subspace lattice algebras. We show that every isometric automorphism of ({{,textrm{Alg},}}{mathcal {L}}) is spatial. We also show that ({{,textrm{Alg},}}{mathcal {L}}) are decomposable, and an operator in ({{,textrm{Alg},}}{mathcal {L}}) is single if and only if it is rank 1 under certain conditions.

Let (rho ) be the defining function of a bounded strongly pseudoconvex domain D with smooth boundary in ({mathbb {C}}^n). In this paper, we study the essential norm of Hankel operators (H^beta _f) which are considered as operators from weighted Bergman spaces (A^p(D,|rho |^alpha ,dV)) to (L^q(D,|rho |^beta ,dV)) with (1<ple q<infty ) and (-1<alpha ,beta <infty ). For (fin L^1(D,|rho |^beta ,dV)), we obtain some quantities in terms of the symbol function f, which are comparable to the essential norm of the Hankel operator (H^beta _f). Furthermore, it is shown that the essential norm of (H^beta _f) is equivalent to the distance norm from itself to compact Hankel operators.

For (mu ge -frac{1}{2}), we show that membership in a space (mathcal {K}_mu ) of type Hankel-(K{M_p}) can be characterized by separate boundedness conditions on a test function and on its (T_{mu , k})-derivatives, where, for every (k in mathbb {N}), (T_{mu , k}=N_{mu +k-1} ldots N_mu ) is a suitable iterate of the Zemanian differential operator (N_mu =x^{mu +frac{1}{2}} D_x x^{-mu -frac{1}{2}}), while (T_{mu , 0}) corresponds to the identity operator. Besides yielding a new representation for the elements, the (weakly, weakly*, strongly) bounded subsets and the (weakly, weakly*, strongly) convergent sequences in the dual space (mathcal {K}_mu ^{prime }), such a characterization ultimately proves that (mathcal {K}_mu ) consists of all those functions in the Zemanian space (mathcal {H}_mu ) whose product against every weight in the defining sequence ({M_p}_{p=0}^infty ) remains bounded.