Annals of Functional Analysis最新文献

It is shown that if A, B, X,  and Y are (ntimes n) complex matrices, such that X and Y are positive semidefinite, then

for (j=1,2,ldots ,n), and if A is accretive–dissipative, then

for every unitarily invariant norm, where (s_{j}left( Tright) ,left| Tright| ), and (omega left( Tright) ) are the (j^{th}) largest singular value of T, the spectral norm of T, and the numerical radius of T, respectively.

The aim of the paper is to discuss and clarify some concepts of the geometric theory of normed spaces. We mainly intend to present recent results concerning the concept of smoothness of normed spaces in connection with the concepts of the strict and uniform convexity of those spaces.

Let ({mathbb {D}}) be the unit disc in the complex plane. Given a positive finite Borel measure (mu ) on the radius [0, 1), we denote the n-th moment of (mu ) as (mu _{n}), that is, (mu _{n}=int _{[0,1)}t^{n} textrm{d}mu (t).) The Cesàro-like operator ({mathcal {C}}_{mu ,s}) is defined on (H({mathbb {D}})) as follows: If (f(z)=sum _{n=0}^{infty }a_{n}z^{n} in H({mathbb {D}} )) then ({mathcal {C}}_{mu ,s}(f)) is defined by

In this paper, our focus is on the action of the (mathrm Cesgrave{a}ro)-type operator ({mathcal {C}}_{mu ,s}) on spaces of analytic functions in ({mathbb {D}}). We characterize the boundedness (compactness) of the (mathrm Cesgrave{a}ro)-like operator ({mathcal {C}}_{mu ,s}), acting between the Bloch space ({mathcal {B}}) and the Bergman space (A^{p}).

We study two constants (g_1(X)) and (J_1(X)) introduced by Fu et al. (Symmetry 13(6):951, 2021), present new characterizations of them, clarify detailed relations of these constants to James and Schäffer constants as well as the relation between (J_1(X)) and (A_2(X)) defined by Baronti et al. (J Math Anal Appl 252(1):124–146, 2000). We also pose several problems.

Let P, Q be two orthogonal projections and J be a symmetry such that (JP=QJ). Based on the block operator technique and Halmos’ CS decomposition, we devote to characterizing the pseudo-regularity of ({mathcal {R}}(P)) and ({mathcal {R}}(Q)). It is given the J-projection onto a regular complement of ({mathcal {R}}(P)^{circ }) in ({mathcal {R}}(P)) (resp. ({mathcal {R}}(Q)^{circ }) in ({mathcal {R}}(Q))). Furthermore, the sets of J-normal projections onto ({mathcal {R}}(P)) and ({mathcal {R}}(Q)) are obtained.

This paper specifically focuses on a specific type of q-difference equations that incorporate multiple delays. The main objective is to explore the existence of positive periodic solutions using coincidence degree theory. Notably, the equation studied in this paper has relevance to important biological growth models constructed on quantum domains. The significance of this research lies in the fact that quantum domains are not translation invariant. By investigating periodic solutions on quantum domains, the paper introduces a new perspective and makes notable advancements in the related literature, which predominantly focuses on translation invariant domains. This research contributes to a better understanding of periodic dynamics in systems governed by q-difference equations with multiple delays, particularly in the context of biological growth models on quantum domains.

We introduce a family of genuine Bernstein–Durrmeyer type operators preserving the functions 1 and (x^j). For them, we establish Voronovskaja type formulas. The behaviour with respect to generalized convex functions is investigated.

In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer’s Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are defined through the affine (L^{p}) functional (mathcal {E}_{p,Omega }^p) introduced by Lutwak et al. (J Differ Geom 62:17–38, 2002) for (p > 1) that is non convex and does not represent a norm in (mathbb {R}^m). Moreover, we address results for discontinuous functional at a point. As an application, we study critical points of the sequence of affine functionals (Phi _m) on a subspace (W_m) of dimension m given by

where (1<alpha <p), ([W_m]_{m in mathbb {N}}) is dense in (W^{1,p}_0(Omega )) and (fin L^{p'}(Omega )), with (frac{1}{p}+frac{1}{p'}=1).

We deal with the Fuglede p-modulus of a system of measures, focusing on three aspects. First, we combine results concerning Badger’s criterion for the extremal function, i.e., the function which realizes the p-modulus, and plans with barycenter in (L^q), which give an alternative—in a sense, probabilistic—approach to p-modulus. It seems that the correlation of these results has not yet been established. Second, we deal with families of measures for which the integral of the extremal function is one. On such a family, the p-modulus as well as the optimal plans are concentrated. We consider closures of these families and relate them with generic families of measures for which the extremal function exists. Finally, we compute the p-modulus and extremal function for finite families of measures.

Let ((X,d,mu )) be an RD-space. In this paper, we prove that a bilinear generalized fractional integral (widetilde{T}_{alpha }) is bounded from the product of generalized Morrey spaces (mathcal {L}^{varphi _{1},p_{1}}(X)times mathcal {L}^{varphi _{2},p_{2}}(X)) into spaces (mathcal {L}^{varphi ,q}(X)), and it is also bounded from the product of spaces (mathcal {L}^{varphi _{1},p_{1}}(X)times mathcal {L}^{varphi _{2},p_{2}}(X)) into generalized weak Morrey spaces (Wmathcal {L}^{varphi ,q}(X)), where the Lebesgue measurable functions (varphi _{1}, varphi _{2}) and (varphi ) satisfy certain conditions and (varphi _{1}varphi _{2}=varphi ), (alpha in (0,1)) and (frac{1}{q}=frac{1}{p_{1}}+frac{1}{p_{2}}-2alpha ) for (1<p_{1}, p_{2}<frac{1}{alpha }). Furthermore, we establish the boundedness of the commutator (widetilde{T}_{alpha ,b_{1},b_{2}}) formed by (b_{1},b_{2}in ) (textrm{BMO}(X)(hbox {or }textrm{Lip}_{beta }(X))) and (widetilde{T}_{alpha }) on spaces (mathcal {L}^{varphi ,q}(X)) and on spaces (Wmathcal {L}^{varphi ,q}(X)). As applications, we show that the (widetilde{T}_{alpha }) and its commutator (widetilde{T}_{alpha ,b_{1},b_{2}}) are bounded on grand generalized Morrey spaces (mathcal {L}^{theta ,varphi ,p)}(X)) over ((X,d,mu )).