we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

This paper presents some new Lie groups preserving fixed subspaces of geometric algebras (or Clifford algebras) under the twisted adjoint representation. We consider cases grades and determined by grade involution reversion. Some considered can be interpreted as generalizations Lipschitz spin groups. The are subgroups these coincide with them in small dimensions. study corresponding algebras.

This paper is concerned with the problem of decomposing a higher order Lipschitz function on closed Jordan curve Γ into sum two polyanalytic functions in each open domain defined by Γ. Our basic tools are Hardy projections related to singular integral operator arising theory, which, as it proved here, represents an involution classes. result generalizes classical decomposition Hölder continuous...

In this paper, we consider inner automorphisms that leave invariant fixed subspaces of real and complex Clifford algebras—subspaces grades determined by the reversion grade involution. We present groups elements define such study their properties. Some these Lie can be interpreted as generalizations Clifford, Lipschitz, spin groups. corresponding algebras. results reformulated for case more gen...

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

We show that any non-degenerate vector field u in L∞(Ω,RN), where Ω is a bounded domain in RN , can be written as u(x) = ∇1H(S(x),x) for a.e. x ∈Ω, where S is a measure preserving point transformation on Ω such that S2 = I a.e (an involution), and H : RN ×RN → R is a globally Lipschitz anti-symmetric convex-concave Hamiltonian. Moreover, u is a monotone map if and only if S can be taken to be t...