Search results for "rete"

A function whose graph has positive doubling measure

2014

We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that the doubling constant of the measure can be chosen to be arbitrarily close to the doubling constant of the Lebesgue measure.

Planar maps whose second iterate has a unique fixed point

2007

Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) t…

Fixed Points in Topological *-Algebras of Unbounded Operators

2001

We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems.

The Spectrum of Analytic Mappings of Bounded Type

2000

Abstract A Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E ′ is weakly compact. For a complex Banach space E and a complex Banach algebra F , let H b ( E ,  F ) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow H b ( E ,  F ) with the usual Frechet topology. M ( H b ( E ,  F ),  F ) denotes the set of all non-null continuous homomorphisms from H b ( E ,  F ) to F . A subset of G EF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets G EF and M ( H b ( E ,  F ),  F ) do not coincide. We prove that if E is symmetrically regu…

Simple and semisimple Lie algebras and codimension growth

1999

Irreducible finitary Lie algebras over fields of positive characteristic

2000

A Lie subalgebra L of [gfr ][lfr ][ ](V) is said to be finitary if it consists of elements of finite rank. We study the situation when L acts irreducibly on the infinite-dimensional vector space V and show: if Char [ ] > 7, then L has a unique minimal ideal I. Moreover I is simple and L/I is solvable.

On complete set of solutions for polynomial matrix equations

1990

Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.

On the additivity of block designs

2016

We show that symmetric block designs $${\mathcal {D}}=({\mathcal {P}},{\mathcal {B}})$$D=(P,B) can be embedded in a suitable commutative group $${\mathfrak {G}}_{\mathcal {D}}$$GD in such a way that the sum of the elements in each block is zero, whereas the only Steiner triple systems with this property are the point-line designs of $${\mathrm {PG}}(d,2)$$PG(d,2) and $${\mathrm {AG}}(d,3)$$AG(d,3). In both cases, the blocks can be characterized as the only k-subsets of $$\mathcal {P}$$P whose elements sum to zero. It follows that the group of automorphisms of any such design $$\mathcal {D}$$D is the group of automorphisms of $${\mathfrak {G}}_\mathcal {D}$$GD that leave $$\mathcal {P}$$P in…

On ergodic operator means in Banach spaces

2016

We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesaro means.

Approximate fixed points of set-valued mapping in b-metric space

2016

We establish existence results related to approximate fixed point property of special types of set-valued contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some fixed point results which generalize and extend various fixed point theorems in the existing literature. A simple example illustrates the new theory. Finally, we apply our results to establishing the existence of solution for some differential and integral problems.