Algebraic Invariants.

1915 ◽  
Vol 22 (1) ◽  
pp. 16
Author(s):  
G. A. Miller ◽  
Leonard Eugene Dickson
Keyword(s):  
Algebraic Invariants

Elements of Spectral Theory for Generalized Derivations II : The Semifredholm Domain

1981 ◽  
Vol 33 (5) ◽  
pp. 1205-1231 ◽  
Author(s):  
Lawrence A. Fialkow
Keyword(s):  
Hilbert Spaces ◽  
Simple Formula ◽  
Decomposition Theorem ◽  
Linear Operators ◽  
Generalized Derivations ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Hilbert Space Operators ◽  
Algebraic Invariants ◽  
Fredholm Theorem

Let and denote infinite dimensional Hilbert spaces and let denote the space of all bounded linear operators from to . For A in and B in , let τAB denote the operator on defined by τAB(X) = AX – XB. The purpose of this note is to characterize the semi-Fredholm domain of τAB (Corollary 3.16). Section 3 also contains formulas for ind(τAB – λ). These results depend in part on a decomposition theorem for Hilbert space operators corresponding to certain “singular points” of the semi-Fredholm domain (Theorem 2.2). Section 4 contains a particularly simple formula for ind(τAB – λ) (in terms of spectral and algebraic invariants of A and B) for the case when τAB – λ is Fredholm (Theorem 4.2). This result is used to prove that (τBA) = –ind(τAB) (Corollary 4.3). We also prove that when A and B are bi-quasi-triangular, then the semi-Fredholm domain of τAB contains no points corresponding to nonzero indices.

scholarly journals Simultaneous approximation of et and ℘(t)

1982 ◽  
Vol 33 (2) ◽  
pp. 171-178
Author(s):  
K. Saradha
Keyword(s):  
Complex Number ◽  
Elliptic Function ◽  
Simultaneous Approximation ◽  
Algebraic Numbers ◽  
Weierstrass Elliptic Function ◽  
Algebraic Invariants ◽  
Image Position

AbstractLet t be any complex number different from the poles of a Weierstrass elliptic function ℘(z), having algebraic invariants. Then we estimate from below the sum where α and β are algebraic numbers. The estimate is given in terms of the heights of α and β and the degree of the field Q(α, β), where Q is the field of rationals.

Rational Equivalence of Fibrations with Fibre G/K

1982 ◽  
Vol 34 (1) ◽  
pp. 31-43 ◽  
Author(s):  
Stephen Halperin ◽  
Jean Claude Thomas
Keyword(s):  
Finite Type ◽  
Homotopy Type ◽  
Lie Group ◽  
The Other ◽  
Homotopy Groups ◽  
Homotopy Equivalence ◽  
Rational Homotopy ◽  
Algebraic Invariants ◽  
Associated Bundles ◽  
Connected Lie Group

Let be two Serre fibrations with same base and fibre in which all the spaces have the homotopy type of simple CW complexes of finite type. We say they are rationally homotopically equivalent if there is a homotopy equivalence between the localizations at Q which covers the identity map of BQ.Such an equivalence implies, of course, an isomorphism of cohomology algebras (over Q) and of rational homotopy groups; on the other hand isomorphisms of these classical algebraic invariants are usually (by far) insufficient to establish the existence of a rational homotopy equivalence.Nonetheless, as we shall show in this note, for certain fibrations rational homotopy equivalence is in fact implied by the existence of an isomorphism of cohomology algebras. While these fibrations are rare inside the class of all fibrations, they do include principal bundles with structure groups a connected Lie group G as well as many associated bundles with fibre G/K.

scholarly journals Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra

2005 ◽  
pp. 19-34 ◽  
Author(s):  
Roberto Bagnara ◽  
Enric Rodríguez-Carbonell ◽  
Enea Zaffanella
Keyword(s):  
Convex Polyhedra ◽  
Algebraic Invariants
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