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 Linear functionals on hypervector spaces

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3031-3043
Author(s):  
O.R. Dehghan
Keyword(s):  
Vector Space ◽  
Linear Algebra ◽  
Linear Functional ◽  
Dual Basis ◽  
Linear Functionals ◽  
Linear Transformations ◽  
Important Special Case ◽  
Finite Dimensional ◽  
Key Topics ◽  
Special Case

The study of linear functionals, as an important special case of linear transformations, is one of the key topics in linear algebra and plays a significant role in analysis. In this paper we generalize the crucial results from the classical theory and study main properties of linear functionals on hypervector spaces. In this way, we obtain the dual basis of a given basis for a finite-dimensional hypervector space. Moreover, we investigate the relation between linear functionals and subhyperspaces and conclude the dimension of the vector space of all linear functionals over a hypervector space, the dimension of sum of two subhyperspaces and the dimension of the annihilator of a subhyperspace, under special conditions. Also, we show that every superhyperspace is the kernel of a linear functional. Finally, we check out whether every basis for the vector space of all linear functionals over a hypervector space V is the dual of some basis for V.

Bounded Linear Functionals on L q

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

scholarly journals Products of two idempotent transformations over arbitrary sets and vector spaces

1998 ◽  
Vol 57 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Rachel Thomas
Keyword(s):  
Vector Space ◽  
Transformation Semigroup ◽  
Vector Spaces ◽  
Endomorphism Monoid ◽  
Linear Transformations ◽  
Arbitrary Vector ◽  
Full Transformation ◽  
Full Transformation Semigroup

In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.

scholarly journals Mackey-complete spaces and power series – a topological model of differential linear logic

2016 ◽  
Vol 28 (4) ◽  
pp. 472-507 ◽  
Author(s):  
MARIE KERJEAN ◽  
CHRISTINE TASSON
Keyword(s):  
Power Series ◽  
Vector Space ◽  
Topological Vector Space ◽  
Taylor Expansion ◽  
Entire Functions ◽  
Linear Logic ◽  
Quantitative Model ◽  
Linear Functions ◽  
Topological Model ◽  
Bounded Linear

In this paper, we describe a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted as bounded linear functions. So as to interpret non-linear proofs of Linear Logic, we use a notion of power series between Mackey-complete spaces, generalizing entire functions in $\mathbb{C}$. Finally, we get a quantitative model of Intuitionist Differential Linear Logic, with usual syntactic differentiation and where interpretations of proofs decompose as a Taylor expansion.

scholarly journals Promotion and Evacuation

10.37236/75 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Richard P. Stanley
Keyword(s):  
Vector Space ◽  
Hecke Algebra ◽  
Linear Extensions ◽  
Linear Transformations ◽  
Basic Properties ◽  
Finite Poset ◽  
Order Ideals ◽  
Maximal Chains

Promotion and evacuation are bijections on the set of linear extensions of a finite poset first defined by Schützenberger. This paper surveys the basic properties of these two operations and discusses some generalizations. Linear extensions of a finite poset $P$ may be regarded as maximal chains in the lattice $J(P)$ of order ideals of $P$. The generalizations concern permutations of the maximal chains of a wider class of posets, or more generally bijective linear transformations on the vector space with basis consisting of the maximal chains of any poset. When the poset is the lattice of subspaces of ${\Bbb F}_q^n$, then the results can be stated in terms of the expansion of certain Hecke algebra products.

Linear Transformations Preserving the Real Orthogonal Group

1975 ◽  
Vol 27 (3) ◽  
pp. 561-572 ◽  
Author(s):  
Albert Wei
Keyword(s):  
Vector Space ◽  
General Problem ◽  
Orthogonal Group ◽  
Linear Transformations ◽  
The Real

Let K be a field and Mn﹛K) denote the vector space of n X n matrices over K. Marcus [4] posed the following general problem: Let W be a subspace of Mn(K) and S a subset of W. Describe the set L(S, W) of all linear transformations T on W such that T(S) is contained in S.

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