Automatic Continuity of Separating Linear Isomorphisms

1990 ◽  
Vol 33 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Krzysztof Jarosz
Keyword(s):  
Automatic Continuity ◽  
Linear Map

AbstractA linear map A : C(T) → C(S) is called separating if f • g ≡ 0 implies Af • Ag = 0. We describe the general form of such maps and prove that any separating isomorphism is continuous.

scholarly journals Automatic continuity of certain isomorphisms between regular Banach function algebras

1997 ◽  
Vol 39 (3) ◽  
pp. 333-343 ◽  
Author(s):  
Juan J. Font
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Linear Map ◽  
Function Algebras ◽  
Commutative Banach Algebras ◽  
Disjointness Preserving ◽  
Banach Function Algebras

AbstractLet A and B be regular semisimple commutative Banach algebras; that is to say, regular Banach function algebras. A linear map T denned from A into B is said to be separating or disjointness preserving if f.g = 0 implies Tf.Tg = 0, for all f, g ∈ A In this paper we prove that if A satisfies Ditkin's condition then a separating bijection is automatically continuous and its inverse is separating. If also B satisfies Ditkin's condition, then it induces a homeomorphism between the structure spaces of A and B.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

scholarly journals A CLASS OF GENES AFFECTING B FACTOR-REGULATED DEVELOPMENT IN SCHIZOPHYLLUM COMMUNE

Genetics ◽  
1976 ◽  
Vol 82 (3) ◽  
pp. 423-428
Author(s):  
Celia Dubovoy
Keyword(s):  
Genetic Factor ◽  
Schizophyllum Commune ◽  
Nuclear Migration ◽  
Complex Pattern ◽  
Developmental Phase ◽  
Linear Map ◽  
Incompatibility Factor ◽  
Complementation Groups ◽  
Cluster A ◽  
Specific Phase

ABSTRACT Twelve mutations affecting nuclear migration, a major developmental phase in Schizophyllum commune, display a complex pattern of complementation and recombination. They are expressed only when a genetic factor controlling this phase of development, the B incompatibility factor, is operative. All twelve mutations are linked to the B factor, nine in a cluster and three in distinct loci outside the cluster. A linear map cannot be constructed from the frequency of recombination. Complementation maps are not linear. There is little correlation between the complementation groups and the groups based on recombination. Many pairs of mutations that do not complement recombine with frequencies of 1.1% to 26.9%. The genes represented by the twelve mutations are located in a linked group of about 18 known genes involved in the specific phase of development controlled by the B factor.

scholarly journals Sur la continuité automatique des épimorphismes dans les☆-algèbres de Banach

2004 ◽  
Vol 2004 (22) ◽  
pp. 1183-1187
Author(s):  
L. Oukhtite ◽  
A. Tajmouati ◽  
Y. Tidli
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Nous Obtenons

Nous étudions les problèmes de continuité automatique dans des algèbres de Banach avec involutions. Nous obtenons aussi des nouveoux résultats concernant☆-idéals des☆-algèbres.We study the automatic continuity problems for Banach algebras with involutions. We also obtain some new results concerning☆-ideals of☆-algebras.

Projective actions, invariant sigma-curves and quadratic functional equations

1985 ◽  
Vol 98 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Patrick J. McCarthy
Keyword(s):  
Functional Equation ◽  
Periodic Function ◽  
Functional Equations ◽  
Continuous Solution ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Continuous Solutions ◽  
Linear Map

AbstractThe quadratic functional equation f(f(x)) *–Tf(x) + Dx = 0 is equivalent to the requirement that the graph be invariant under a certain linear map The induced projective map is used to show that the equation admits a rich supply of continuous solutions only when L is hyperbolic (T2 > 4D), and then only when T and D satisfy certain further conditions. The general continuous solution of the equation is given explicitly in terms of either (a) an expression involving an arbitrary periodic function, function additions, inverses and composites, or(b) suitable limits of such solutions.

scholarly journals Existence of an invariant form under a linear map

2017 ◽  
Vol 48 (2) ◽  
pp. 211-220 ◽  
Author(s):  
Krishnendu Gongopadhyay ◽  
Sudip Mazumder
Keyword(s):  
Invariant Form ◽  
Linear Map
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