Let X,Y be locally convex spaces and L(X,Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series P Tk in L(X,Y ). First, if λ is a scalar sequence space, we say that the series P Tk is λ multiplier convergent for a locally convex topology τ on L(X,Y ) if the series P tkTk is τ convergent for every t = {tk} ∈ λ. We establish...

We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or H-limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular H-limit are projective and inductive limits of separated locally convex spaces. The class of H-spaces contains Fréchet spaces and is stable under forming countable inductive and projective limits, closed subspaces and quo...

Recently, locally semiconcave control Lyapunov functions (LS-CLFs) play important roles in nonlinear control theory. Many LS-CLF based stabilizing controllers are proposed. In this paper, we consider the locally asymptotic stabilization problem of the input affine nonlinear systems with convex input constraints. To design a stabilizing state feedback under the input constraints, we employ the L...

The well-known results about the existence of separable, measurable resp., modifications of stochastic processes (e.g., [4, 5]) are generalized to the case of real valued random fields indexed by a separable, separable and locally convex resp., metric space.

It is well known that every normed (even quasibarrelled) space a Mackey space. However, in the more general realm of locally quasi-convex abelian groups an analogous result does not hold. We give first examples spaces which are groups.

We present Kakutani type fixed point theorems for certain semigroups of self maps by relaxing conditions on the underlying set, family of self maps, and the mappings themselves in a locally convex space setting.

We discuss positive Miyadera–Voigt type perturbations for bi-continuous semigroups on \(\mathrm {AL}\)-spaces with an additional locally convex topology generated by additive seminorms. The main example of such spaces is the space bounded Borel measures (on a Polish space).

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we giv...

For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn , let K(Y ) be the family of all fuzzy sets of Rn , which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space K(Y ) with the topology of endograph metric is homeomorphic to the Hilbert cube Q = [−1, 1] iff Y is compact; and the space K(Y ) is homeomorphic to {(...

We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of c0 and superreflexivity are discussed. The question of coarse embeddability into uniformly convex Banach spaces became interesting after the recent work of G. Kasparov and G. Yu, who showed the coarse Novi...