Related papers: Polyak's theorem on Hilbert spaces

In this work we will investigate a certain generalization of the so called S-lemma in higher degrees. The importance of this generalization is, that it is closely related to Hilbert's 1888 theorem about tenary quartics. In fact, if such a…

Hille's theorem is a powerful classical result in vector measure theory. It asserts that the application of a closed, unbounded linear operator commutes with strong/Bochner integration of functions taking values in a Banach space. This note…

We study the boundary behavior of functions in the Hardy spaces on the infinite dimensional polydisk. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several Fatou and Marcinkiewicz-Zygmund type…

We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…

We prove a version of the Bernstein-Walsh theorem on uniform polynomial approximation of holomorphic functions on compact sets in several complex variables. Here we consider subclasses of the full polynomial space associated to a convex…

We prove that every functor from the category of Hilbert spaces and linear isometric embeddings to the category of sets which preserves directed colimits must be essentially constant on all infinite-dimensional spaces. In other words, every…

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In…

It is shown that any smooth closed orientable manifold of dimension $2k + 1$, $k \geq 2$, admits a smooth polynomially convex embedding into $\mathbb C^{3k}$. This improves by $1$ the previously known lower bound of $3k+1$ on the possible…

This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

We lift upper and lower estimates from linear functionals to $n$-homogeneous polynomials and using this result show that $l_\infty$ is finitely represented in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite dimensional…

In this paper, we give three different new proofs of the validity of the geometry conjecture about cycles of projections onto nonempty closed, convex subsets of a Hilbert space. The first uses a simple minimax theorem, which depends on the…

We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of $0$-symmetric convex bodies in Euclidean spaces. We prove that there is a bijection between tensor products of…

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward…

We describe the multiplier algebra of the noncommutative Schwartz space. This multiplier algebra can be seen as the largest ${}^*$-algebra of unbounded operators on a separable Hilbert space with the classical Schwartz space of rapidly…

In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is…

We show a Dvoretsky-Rogers type Theorem for the adapted version of the $q$-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the…

We show a Wolff-Denjoy type theorem in complete geodesic spaces in the spirit of Beardon's framework that unifies several results in this area. In particular, it applies to strictly convex bounded domains in $\mathbb{R}^{n}$ or…

We prove Nehari's theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the…

We propose an algorithm for computing the proximity operator of a sum of composite convex functions in Hilbert spaces and investigate its asymptotic behavior. Applications to best approximation and image recovery are described.