scholarly journals A CLOSED ALGEBRA OF CLEBSCH FORMS DERIVED FROM WHITTAKER SUPER-POTENTIALS AND APPLICATIONS IN ELECTROMAGNETIC RESEARCH.

2013 ◽  
Vol 42 ◽  
pp. 97-107
Author(s):  
Theophanes E. Raptis
Keyword(s):  
Closed Algebra

Simultaneous Triangularization of Algebras of Polynomially Compact Operators

1991 ◽  
Vol 34 (2) ◽  
pp. 260-264 ◽  
Author(s):  
M. Radjabalipour
Keyword(s):  
Hilbert Space ◽  
Jacobson Radical ◽  
Compact Operators ◽  
General Algebra ◽  
Closed Algebra ◽  
Quasinilpotent Operators ◽  
Simultaneous Triangularization

AbstractIf A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.

Pseudocomplemented and Implicative Semilattices

1982 ◽  
Vol 34 (2) ◽  
pp. 423-437 ◽  
Author(s):  
C. S. Hoo
Keyword(s):  
Boolean Algebra ◽  
Closed Algebra ◽  
Implicative Semilattices

Let L be a semilattice and let a ∊ L. We refer the reader to Definitions 2.2, 2.4, 2.5 and 2.12 below for the terminology. If L is a-implicative, let Ca be the set of a-closed elements of L, and let Da be the filter of a-dense elements of L. Then Ca is a Boolean algebra. If a = 0, then C0 and D0 are the usual closed algebra and dense filter of L. If L is a-admissible and f : Ca × Da → Da is the corresponding admissible map, we can form a quotient semilattice Ca × D0f. In case a = 0, Murty and Rao [4] have shown that C0 × D0/f is isomorphic to L, and hence that C0 × D0 is 0-admissible. In case L is in fact implicative, Nemitz [5] has shown that C0 × D0/f is isomorphic to L, and that C0 × D0/f is also implicative.

On Quasisimilarity for Subnormal Operators, II

1982 ◽  
Vol 25 (1) ◽  
pp. 37-40 ◽  
Author(s):  
John B. Conway
Keyword(s):  
Subnormal Operator ◽  
Unilateral Shift ◽  
Closed Algebra ◽  
Subnormal Operators ◽  
Weak Star

AbstractLet S be a subnormal operator and let be the weak-star closed algebra generated by S and 1. An example of an irreducible cyclic subnormal operator S is found such that there is a T in with S and T quasisimilar but not unitarily equivalent. However, if S is the unilateral shift, T ∈ and S and T are quasisimilar, then S ≅ T.

On Operator Algebras and Invariant Subspaces

1969 ◽  
Vol 21 ◽  
pp. 1178-1181 ◽  
Author(s):  
Chandler Davis ◽  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Hilbert Space ◽  
Elementary Proof ◽  
Operator Algebras ◽  
Equivalent Form ◽  
Invariant Subspaces ◽  
Complex Hilbert Space ◽  
Closed Algebra ◽  
Weakly Closed ◽  
Special Case

If is a collection of operators on the complex Hilbert space , then the lattice of all subspaces of which are invariant under every operator in is denoted by Lat . An algebra of operators on is defined (3; 4) to be reflexive if for every operator B on the inclusion Lat ⊆ Lat B implies .Arveson (1) has proved the following theorem. (The abbreviation “m.a.s.a.” stands for “maximal abelian self-adjoint algebra”.)ARVESON's THEOREM. Ifis a weakly closed algebra which contains an m.a.s.a.y and if Lat, then is the algebra of all operators on .A generalization of Arveson's Theorem was given in (3). Another generalization is Theorem 2 below, an equivalent form of which is Corollary 3. This theorem was motivated by the following very elementary proof of a special case of Arveson's Theorem.

Generators of Nest Algebras

1974 ◽  
Vol 26 (3) ◽  
pp. 565-575 ◽  
Author(s):  
W. E. Longstaff
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Nest Algebra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Algebra ◽  
Nest Algebras ◽  
Weakly Closed

A collection of subspaces of a Hilbert space is called a nest if it is totally ordered by inclusion. The set of all bounded linear operators leaving invariant each member of a given nest forms a weakly-closed algebra, called a nest algebra. Nest algebras were introduced by J. R. Ringrose in [9]. The present paper is concerned with generating nest algebras as weakly-closed algebras, and in particular with the following question which was first raised by H. Radjavi and P. Rosenthal in [8], viz: Is every nest algebra on a separable Hilbert space generated, as a weakly-closed algebra, by two operators? That the answer to this question is affirmative is proved by first reducing the problem using the main result of [8] and then by using a characterization of nests due to J. A. Erdos [2].

ANOMALOUS GAUSS LAW ALGEBRAS

1989 ◽  
Vol 04 (17) ◽  
pp. 4581-4591 ◽  
Author(s):  
R. FLOREANINI ◽  
R. PERCACCI
Keyword(s):  
Gauge Theory ◽  
Lie Algebra ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Abelian Extensions ◽  
Closed Algebra

Supplementing the Gauss law operator of an anomalous gauge theory with a certain set of functionals of the gauge potentials, one obtains a closed algebra. The algebras obtained in this way are Abelian extensions of the Lie algebra of the group of gauge transformations, and are natural generalizations of Kac-Moody algebras, both in two and four dimensions.

scholarly journals GAUGING OF CHERN-SIMONS p-BRANES

1994 ◽  
Vol 09 (19) ◽  
pp. 3367-3375 ◽  
Author(s):  
RAIKO P. ZAIKOV
Keyword(s):  
Phase Space ◽  
Poisson Bracket ◽  
Target Space ◽  
Closed Algebra ◽  
Chern Simons ◽  
Infinite Set

The Chern-Simons membranes and in general the Chern-Simons p-branes moving in D-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket these constraints form a closed algebra which contains the classical W1+∞ algebra in p dimensions as a subalgebra. A corresponding gauged theory in the phase space is constructed in a Hamiltonian gauge as an analog of the ordinary W gravity.

scholarly journals SUPERSPACE FORMULATION FOR THE BRST QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1998 ◽  
Vol 13 (03) ◽  
pp. 493-500 ◽  
Author(s):  
EVERTON M. C. ABREU ◽  
NELSON R. F. BRAGA
Keyword(s):  
Gauge Theories ◽  
Brst Quantization ◽  
Loop Order ◽  
Schwinger Model ◽  
Closed Algebra ◽  
Quantum Action

It has recently been shown that the field–antifield quantization of anomalous irreducible gauge theories with closed algebra can be represented in a BRST superspace where the quantum action at one loop order, including the Wess–Zumino term, and the anomalies show up as components of the same superfield. We show here how the Chiral Schwinger Model can be represented in this formulation.

On Reflexivity of Algebras

1981 ◽  
Vol 33 (6) ◽  
pp. 1291-1308 ◽  
Author(s):  
Mehdi Radjabalipour
Keyword(s):  
Hilbert Space ◽  
Natural Number ◽  
Separable Hilbert Space ◽  
Invariant Subspaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Algebra ◽  
Direct Sum ◽  
Weakly Closed

For each natural number n we define to be the class of all weakly closed algebras of (bounded linear) operators on a separable Hilbert space H such that the lattice of invariant subspaces of and (alg lat )(n) are the same. (If A is an operator, A(n) denotes the direct sum of n copies of A; if is a collection of operators,. Also, alg lat denotes the algebra of all operators leaving all invariant subspaces of invariant.) In the first section we show that . In Section 2 we prove that every weakly closed algebra containing a maximal abelian self adjoint algebra (m.a.s.a.) is , and that . It is also shown that certain algebras containing a m.a.s.a. are necessarily reflexive.

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