Bounded Linear Functionals on L q

1965 ◽  
Vol 72 (7) ◽  
pp. 750
Author(s):  
W. Fulks
Keyword(s):  
Linear Functionals ◽  
Bounded Linear

scholarly journals Completion of normed algebras of polunomials

1975 ◽  
Vol 20 (4) ◽  
pp. 504-510 ◽  
Author(s):  
H. G. Dales ◽  
J. P. McClure
Keyword(s):  
Power Series ◽  
Banach Algebra ◽  
Formal Power Series ◽  
Complex Field ◽  
Linear Functionals ◽  
Bounded Linear ◽  
One To One ◽  
Formal Power

Let P be the algebra of polynomials in one inderminate x over the complex field C. Suppose ∥ · ∥ is a norm on P such that the coefficient functionals cj: ∑αix1 → αj (j = 0,1,2,…) are all continuous with respect to ∥·∥, and Let K ⊂ C be the set of characters on P which are ∥·∥-continuous. then K is compact, C\K is connected, and 0∈K. K. Let A be the completion of P with respect to ∥·∥. Then A is a singly generated Banach algebra, with space of characters (homeomorphic with) K. The functionals cj have unique extensions to bounded linear functionals on A, and the map a →∑Ci(a)xi (a ∈ A) is a homomorphism from A onto an algebra of formal power series with coefficients in C. We say that A is an algebra of power series if this homomorphism is one-to-one, that is if a ∈ A and a≠O imply cj(a)≠ 0 for some j.

On Order Properties of Order Bounded Transformations

1975 ◽  
Vol 27 (3) ◽  
pp. 666-678 ◽  
Author(s):  
Charalambos D. Aliprantis
Keyword(s):  
Vector Space ◽  
Riesz Space ◽  
Linear Functionals ◽  
Linear Transformations ◽  
Bounded Linear

W. A. J. Luxemburg and A. C. Zaanen in [7] and W. A. J. Luxemburg in [5] have studied the order properties of the order bounded linear functionals of a given Riesz space L. In this paper we consider the vector space (L, M) of the order bounded linear transformations from a given Riesz space L into a Dedekind complete Riesz space M.

scholarly journals On the extension of linear operators

2001 ◽  
Vol 28 (10) ◽  
pp. 621-623 ◽  
Author(s):  
John J. Saccoman
Keyword(s):  
Extension Theorem ◽  
Linear Operators ◽  
Two Dimensional ◽  
Linear Functionals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Banach Theorem

It is well known that the Hahn-Banach theorem, that is, the extension theorem for bounded linear functionals, is not true in general for bounded linear operators. A characterization of spaces for which it is true was published by Kakutani in 1940. We summarize Kakutani's work and we give an example which demonstrates that his characterization is not valid for two-dimensional spaces.

scholarly journals Order-bounded convergence structures on spaces of continuous functions

1979 ◽  
Vol 28 (1) ◽  
pp. 39-61 ◽  
Author(s):  
M. Schroder
Keyword(s):  
Vector Lattice ◽  
Continuous Functions ◽  
Subject Classification ◽  
Linear Functionals ◽  
Bounded Linear ◽  
Spaces Of Continuous Functions ◽  
Locally Convex Topologies ◽  
Locally Convex ◽  
Compact Convergence

AbstractThis paper deals with solid topologies and convergence structures on the vector-lattice CX (the set of all continuous real-valued functions on a space X): the closed ideals and locally convex topologies associated with such structures are studied in particular. The work stems from E. Hewitt's paper on bounded linear functionals, touches on the classical theorems of L. Nachbin, T. Shirota and others (determining when the topology of compact convergence is barrelled or bornological), and extends some recent results on the duality between x and CX.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 35; secondary 54 A 20.

scholarly journals Topological duals of some paranormed sequence spaces

2003 ◽  
Vol 2003 (30) ◽  
pp. 1883-1897
Author(s):  
Nandita Rath
Keyword(s):  
Sequence Spaces ◽  
Positive Sequence ◽  
Infinite Matrix ◽  
Linear Functionals ◽  
Normed Spaces ◽  
General Representation ◽  
Bounded Linear ◽  
Special Cases ◽  
The Matrix ◽  
Almost All

LetP=(pk)be a bounded positive sequence and letA=(ank)be an infinite matrix with allank≥0. For normed spacesEandEk, the matrixAgenerates the paranormed sequence spaces[A,P]∞((Ek)),[A,P]0((Ek)), and[A,P]((E)), which generalise almost all the well-known sequence spaces such asc0,c,lp,l∞, andwp. In this paper, topological duals of these paranormed sequence spaces are constructed and general representation formulae for their bounded linear functionals are obtained in some special cases of matrixA.

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