scholarly journals A generalization of Lagrange multipliers: Corrigendum

1978 ◽  
Vol 18 (1) ◽  
pp. 159-160
Author(s):  
B.D. Craven
Keyword(s):  
Banach Spaces ◽  
Lagrange Multipliers ◽  
Continuous Linear ◽  
Linear Map ◽  
Linear Maps ◽  
Valid Proof

There is a lacuna in the proof of Lemma 1 of [1]; the projector q is assumed without proof. An alternative, valid proof is as follows.LEMMA 1. Let S, U0, V0 be real Banach spaces; let A : S → U0 and B : S → V0 be continuous linear maps, whose null spaces are N(A) respectively N(B); let N(A) ⊂ N(B) : let A map S onto U0. Then there exists a continuous linear map C : U0 → V0 such that B = C ° A.

Spaces of operators between Fréchet spaces

1994 ◽  
Vol 115 (1) ◽  
pp. 133-144 ◽  
Author(s):  
José Bonet ◽  
Mikael Lindström
Keyword(s):  
Banach Spaces ◽  
Compact Operators ◽  
Fréchet Spaces ◽  
Continuous Linear ◽  
Linear Map ◽  
Linear Maps ◽  
Spaces Of Operators ◽  
Space Of Compact Operators ◽  
Compact Subsets

AbstractMotivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson–Nissenzweig theorem to Fréchet spaces, we investigate pairs of Fréchet spaces (E, F) such that every continuous linear map from E into F is Montel, i.e. it maps bounded subsets of E into relatively compact subsets of F. As a consequence of our results we characterize pairs of Köthe echelon spaces (E, F) such that the space of Montel operators from E into F is complemented in the space of all continuous linear maps from E into F.

scholarly journals On the surjectivity of linear maps on locally convex spaces

1982 ◽  
Vol 32 (2) ◽  
pp. 187-211 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Basic Notion ◽  
Linear Map ◽  
Linear Maps ◽  
Locally Convex ◽  
Do So ◽  
Convex Spaces

AbstractThe aim of this note is to investigate the structure of general surjectivity problem for a continuous linear map between locally convex spaces. We shall do so by using the method introduced in Yamamuro (1980). Its basic notion is that of calibrations which has been introduced in Yamamuro (1975), studied in detail in Yamamuro (1979) and appliced to several problems in Yamamuro (1978) and Yamamuro (1979a).

scholarly journals A generalization of Lagrange multipliers

1970 ◽  
Vol 3 (3) ◽  
pp. 353-362 ◽  
Author(s):  
B. D. Craven
Keyword(s):  
Banach Spaces ◽  
Lagrange Multipliers ◽  
Lagrange Equation ◽  
Linear Mapping ◽  
Real Field ◽  
Dimensional Problem ◽  
Continuous Linear ◽  
Continuous Linear Mapping ◽  
Finite Dimensional ◽  
Method Of Lagrange Multipliers

The method of Lagrange multipliers for solving a constrained stationary-value problem is generalized to allow the functions to take values in arbitrary Banach spaces (over the real field). The set of Lagrange multipliers in a finite-dimensional problem is shown to be replaced by a continuous linear mapping between the relevant Banach spaces. This theorem is applied to a calculus of variations problem, where the functional whose stationary value is sought and the constraint functional each take values in Banach spaces. Several generalizations of the Euler-Lagrange equation are obtained.

scholarly journals Closed linear maps from a barrelled normed space into itself need not be continuous

1998 ◽  
Vol 57 (2) ◽  
pp. 177-179 ◽  
Author(s):  
José Bonet
Keyword(s):  
Normed Space ◽  
Continuous Linear ◽  
Closed Graph ◽  
Linear Map ◽  
Linear Maps ◽  
Barrelled Spaces

Examples of normed barrelled spacesEor quasicomplete barrelled spacesEare given such that there is a non-continuous linear map from the spaceEinto itself with closed graph.

Topological decompositions of the duals of locally convex operator spaces

1983 ◽  
Vol 93 (2) ◽  
pp. 307-314 ◽  
Author(s):  
D. J. Fleming ◽  
D. M. Giarrusso
Keyword(s):  
Uniform Convergence ◽  
Banach Spaces ◽  
Linear Subspace ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Operator Spaces ◽  
Natural Topology ◽  
Usual Norm ◽  
Linear Maps ◽  
Locally Convex

If Z and E are Hausdorff locally convex spaces (LCS) then by Lb(Z, E) we mean the space of continuous linear maps from Z to E endowed with the topology of uniform convergence on the bounded subsets of Z. The dual Lb(Z, E)′ will always carry the topology of uniform convergence on the bounded subsets of Lb(Z, E). If K(Z, E) is a linear subspace of L(Z, E) then Kb(Z, E) will be used to denote K(Z, E) with the relative topology and Kb(Z, E)″ will mean the dual of Kb(Z, E)′ with the natural topology of uniform convergence on the equicontinuous subsets of Kb(Z, E)′. If Z and E are Banach spaces these provide, in each instance, the usual norm topologies.

scholarly journals Preregular maps between Banach lattices

1974 ◽  
Vol 11 (2) ◽  
pp. 231-254 ◽  
Author(s):  
David A. Birnbaum
Keyword(s):  
Banach Lattice ◽  
Vector Lattice ◽  
Banach Lattices ◽  
Continuous Linear ◽  
Index Set ◽  
Linear Map ◽  
Linear Maps ◽  
The Difference

A continuous linear map from a Banach lattice E into a Banach lattice F is preregular if it is the difference of positive continuous linear maps from E into the bidual F″ of F. This paper characterizes Banach lattices B with either of the following properties:(1) for any Banach lattice E, each map in L(E, B) is preregular;(2) for any Banach lattice F, each map in L(B, F) is preregular.It is shown that B satisfies (1) (repectively (2)) if and only if B′ satisfies (2) (respectively (1)). Several order properties of a Banach lattice satisfying (2) are discussed and it is shown that if B satisfies (2) and if B is also an atomic vector lattice then B is isomorphic as a Banach lattice to 11(Γ) for some index set Γ.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Continuous Linear Maps

2014 ◽  
pp. 115-138
Author(s):  
Joseph Muscat
Keyword(s):  
Continuous Linear ◽  
Linear Maps

scholarly journals Linear maps on *-algebras acting on orthogonal elements like derivations or anti-derivations

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4543-4554 ◽  
Author(s):  
H. Ghahramani ◽  
Z. Pan
Keyword(s):  
Linear Map ◽  
Unital Algebra ◽  
C Algebras ◽  
Orthogonality Conditions ◽  
Linear Maps ◽  
Unital Simple

Let U be a unital *-algebra and ? : U ? U be a linear map behaving like a derivation or an anti-derivation at the following orthogonality conditions on elements of U: xy = 0, xy* = 0, xy = yx = 0 and xy* = y*x = 0. We characterize the map ? when U is a zero product determined algebra. Special characterizations are obtained when our results are applied to properly infinite W*-algebras and unital simple C*-algebras with a non-trivial idempotent.

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