Annals of Functional Analysis最新文献

Let (mu) be a Radon measure on ({mathbb {R}}^{d}) which may be non-doubling and only satisfies (mu (Q(x,l))le C_{0}l^{n}) for all (xin {mathbb {R}}^{d}), (l(Q)>0), with some fixed constants (C_{0}>0) and (nin (0,d]). We introduce a new type of (bmo(mu )) space which looks bigger than the (rbmo(mu )) space of Dachun Yang(JAMS, 2005). And its four equivalent norms are established by constructing some special types of auxiliary doubling cubes. Then we further obtain that this new (rbmo(mu )) space actually coincides with the (rbmo(mu )) space of Dachun Yang.

We study Köthe PDF-algebras. Using two (different yet natural) definitions of multiplication we obtain a wide class of natural algebras with either discontinuous or continuous multiplication. In this last case, we are able to fully characterize amenable Köthe PDF-algebras in terms of the defining Köthe matrix. This characterization shows an interesting and unexpected relation between algebraic and topological structures of amenable Köthe PDF-algebras.

We analyze a notion of (C^*)-independence for ({mathbb {Z}}_2)-graded (C^*)-algebras. We provide other notions of statistical independence for ({mathbb {Z}}_2)-graded von Neumann algebras and prove some relationships between them. We provide a characterization for the graded nuclearity property.

It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto intervals or in other words, consecutive terms of ({mathbb {N}}.) In this paper, we fix a sequence ((a_n)_{n=1}^infty ) and compare the TGA against projections onto consecutive terms of the sequence and its shifts. We call the corresponding greedy-type condition the ({mathcal {F}}_{(a_n)})-almost greedy property. Our first result shows that the ({mathcal {F}}_{(a_n)})-almost greedy property is equivalent to the classical almost greedy property if and only if ((a_n)_{n=1}^infty ) is bounded. Then we establish an analog of the result for the strong partially greedy property. Finally, we show that under a certain projection rule and conditions on the sequence ((a_n)_{n=1}^infty ,) we obtain a greedy-type condition that lies strictly between the almost greedy and strong partially greedy properties.

We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel statement for homogeneous bundles without the metrizability assumption, and generalizes the analogous result to the effect that subhomogeneous (C^*) bundles over compact metrizable spaces admit finite-index expectations.

The purpose of this note is to characterize the reducibility and the n-hypercontractivity of extensions of Cowen–Douglas operators, and to show that the two have a mutually determining relationship in this context. In doing so, the curvature of the Hermitian holomorphic vector bundle is considered. Let (mathcal {F}B_k(Omega )) denote the class of Cowen–Douglas operators with flag structure and index k. As an important class of geometric operators, these operators have been studied extensively in recent research. It has been proven to be norm dense in the Cowen–Douglas operator class with index k. As applications, we provide a sufficient condition that operators in (mathcal {F}B_k(Omega )) are not n-hypercontractive.

Given a Banach lattice L,  the space of lattice Lipschitz operators on L has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is a particular space of superposition operators on Banach lattices. Motivated by certain procedures in Reinforcement Learning based on McShane–Whitney extensions of Lipschitz maps, this class has proven to be useful also in the classical context of Mathematical Analysis. In this paper, we discuss the properties of such operators when defined on spaces of continuous functions, focusing attention on the functional bounds for the pointwise Lipschitz inequalities defining the lattice Lipschitz operators, the representation theorems for these operators as vector-valued functions, and the corresponding dual spaces. Finally, and with possible applications in Artificial Intelligence in mind, we provide a McShane–Whitney extension theorem for these operators.

A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the problem admits solutions for every initial data (in an adequate set).

A mixed polynomial, or a Hermitian polynomial, is a (multivariate) complex polynomial with monomials in complex variables and their conjugates. This paper deals with two types of mixed polynomials: sums of squared magnitudes of mixed polynomials (SOS polynomials for short) and those of usual complex polynomials (shortly, SQN polynomials). It is obvious that SQN polynomials are SOS, but generally, the converse is invalid. Both SOS and SQN polynomials are always mixed ones. This paper aims to provide sufficient and necessary conditions for a mixed polynomial to be SOS or SQN via moment matrices and the polynomial degree. We then give a sufficient condition for a SOS polynomial to be SQN, based on its degree. To this end, we apply the flat extension theory to the moment matrices of SOS and SQN polynomials and consider some optimization problems over positive linear functionals defined on the (*)-vector space of these two polynomial types. Consequently, we also give a degree characteristic of polynomials in the radical of the SQN set, which is one of the interesting problems posed by D’Angelo (Adv Math 226:4607–4637, 2011). An application in quantum information is also discussed: We introduce a class of quantum matrices whose degree-four SQN polynomials simultaneously satisfy the nonnegative, SQN and SOS properties.

This paper analyzes, by employing topological approaches, the solvability of equations and systems involving p-k-Hessian operator. We first provide sufficient conditions for the existence of infinitely many p-k-convex solutions for a p-k-Hessian equation. Then we discuss the existence of infinitely many p-k-convex solutions for a p-k-Hessian system. We also study the existence of three infinite families of p-k-convex solutions for p-k-Hessian equations and systems. An example is presented to illustrate the applicability of our main results.