scholarly journals The Tensor Product Representation of Polynomials of Weak Type in a DF-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Masaru Nishihara ◽  
Kwang Ho Shon
Keyword(s):  
Tensor Product ◽  
Weak Type ◽  
Symmetric Tensor ◽  
Homogeneous Polynomials ◽  
Product Representation ◽  
Bounded Set ◽  
Weakly Continuous ◽  
Tensor Product Space ◽  
Locally Convex ◽  
Tensor Product Representation

LetEandFbe locally convex spaces overCand letP(nE;F)be the space of all continuousn-homogeneous polynomials fromEtoF. We denote by⨂n,s,πEthen-fold symmetric tensor product space ofEendowed with the projective topology. Then, it is well known that each polynomialp∈P(nE;F)is represented as an element in the spaceL(⨂n,s,πE;F)of all continuous linear mappings from⨂n,s,πEtoF. A polynomialp∈P(nE;F)is said to beof weak typeif, for every bounded setBofE,p|Bis weakly continuous onB. We denote byPw(nE;F)the space of alln-homogeneous polynomials of weak type fromEtoF. In this paper, in case thatEis a DF space, we will give the tensor product representation of the spacePw(nE;F).

scholarly journals ON THE BREATHERS OF $a_n^{(1)} $ AFFINE TODA FIELD THEORY

1995 ◽  
Vol 10 (13) ◽  
pp. 1879-1903 ◽  
Author(s):  
ULI HARDER ◽  
ALEXANDER A. ISKANDAR ◽  
WILLIAM A. McGHEE
Keyword(s):  
Field Theory ◽  
Tensor Product ◽  
Topological Charge ◽  
Product Representation ◽  
Explicit Constructions ◽  
First Case ◽  
The Masses ◽  
Topological Charges ◽  
Tensor Product Representation ◽  
Toda Field Theory

Explicit constructions [Formula: see text] of affine Toda field theory breather solutions are presented. Breathers arise either from two solitons of the same species or from solitons which are antispecies of each other. In the first case, breathers carry topological charges. These topological charges lie in the tensor product representation of the fundamental representations associated with the topological charges of the constituent solitons. In the second case, breathers have zero topological charge. The breather masses are, as expected, less than the sum of the masses of the constituent solitons.

Tensor-product representation of qubits and tensor realization of one-qubit operators

2013 ◽  
Vol T153 ◽  
pp. 014001 ◽  
Author(s):  
Peter Adam ◽  
Vladimir A Andreev ◽  
Jozsef Janszky ◽  
Margarita A Man'ko ◽  
Vladimir I Man'ko
Keyword(s):  
Tensor Product ◽  
Product Representation ◽  
Tensor Product Representation

scholarly journals TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE Lp-SPACE OF A VECTOR MEASURE

2009 ◽  
Vol 87 (2) ◽  
pp. 211-225 ◽  
Author(s):  
IRENE FERRANDO ◽  
ENRIQUE A. SÁNCHEZ PÉREZ
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Normed Space ◽  
Dual Space ◽  
Vector Measure ◽  
Real Numbers ◽  
Product Representation ◽  
Lp Space ◽  
Integrable Functions ◽  
Tensor Product Representation

AbstractThe duality properties of the integration map associated with a vector measure m are used to obtain a representation of the (pre)dual space of the space Lp(m) of p-integrable functions (where 1<p<∞) with respect to the measure m. For this, we provide suitable topologies for the tensor product of the space of q-integrable functions with respect to m (where p and q are conjugate real numbers) and the dual of the Banach space where m takes its values. Our main result asserts that under the assumption of compactness of the unit ball with respect to a particular topology, the space Lp(m) can be written as the dual of a suitable normed space.

Anosov automorphisms for nilmanifolds and rigidity of group actions

1995 ◽  
Vol 15 (2) ◽  
pp. 341-359 ◽  
Author(s):  
Nantian Qian
Keyword(s):  
Tensor Product ◽  
Lyapunov Exponents ◽  
Finite Index ◽  
Group Actions ◽  
Irreducible Representations ◽  
Product Representation ◽  
Tensor Product Representation

AbstractWe obtain the density of Lyapunov exponents for maximal abelian ℝ-split group in kth tensor product representation of a subgroup Γ ⊂ SL(n, ℤ) of finite index under certain conditions. Anosov and Cartan actions of such groups associated with irreducible representations of SL(n, ℝ) are also classified. Examples of rigidity of actions on nilmanifolds are discussed.

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