scholarly journals A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1512
Author(s):  
Juan Luis García Guirao ◽  
Mobashir Iqbal ◽  
Zia Bashir ◽  
Tabasam Rashid
Keyword(s):  
Riesz Space ◽  
Linear Operators ◽  
Separation Property ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Spaces ◽  
Fuzzy Order ◽  
Locally Convex ◽  
Special Case

This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.

scholarly journals Extension and inversion of extended orthomorphisms on Riesz spaces

1984 ◽  
Vol 37 (2) ◽  
pp. 223-242 ◽  
Author(s):  
Michel Duhoux ◽  
Mathieu Meyer
Keyword(s):  
Riesz Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Dense Ideal ◽  
Riesz Spaces ◽  
Dense Domain ◽  
And Inversion

AbstractLet E be an Archimedean Riesz space and let Orth∞(E) be the f-algebra consisting of all extended orthomorphisms on E, that is, of all order bounded linear operators T:D→E, with D an order dense ideal in E, such that T(B∩D) ⊆ B for every band B in E. We give conditions on E and on a Riesz subspace F of E insuring that every T ∈ Orth∞(F) can be extended to some ∈ Orth∞(E), and we also consider the problem of inversing an extended orthomorphism on its support. The same problems are also studied in the case of σ-orthomorphisms, that is, extended orthomorphisms with a super order dense domain. Furthermore, some applications are given.

scholarly journals A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS

1990 ◽  
Vol 21 (4) ◽  
pp. 395-398
Author(s):  
BORIS LAVRIČ
Keyword(s):  
Weak Form ◽  
Riesz Space ◽  
Linear Operators ◽  
Spectral Theorem ◽  
Bounded Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Spaces

Let $L$, $M$ be Archimedean Riesz spaces with $M$ Dedekind complete, and let $\mathcal L_b(L,M )$ be the Riesz space of order bounded linear operators from $L$ into $M$. A theorem of Abramovic [1] on lattice operations of $\mathcal L_b(L,M )$ is generalized on Riesz spaces $L$ in which a weak form of Freudenthal's spectral theorem [4] holds.

scholarly journals On mixed C-semigroups of operators on Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2673-2682
Author(s):  
Masoud Mosallanezhad ◽  
Mohammad Janfada
Keyword(s):  
Banach Spaces ◽  
Parameter Family ◽  
Linear Operators ◽  
Semigroups Of Operators ◽  
Semigroup Of Operators ◽  
Cauchy Equation ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Special Case

In this paper an H-generalized Cauchy equation S(t+s)C = H(S(s),S(t)) is considered, where {S(t)}t?0 is a one parameter family of bounded linear operators and H : B(X) x B(X) ? B(X) is a function. In the special case, when H(S(s), S(t))=S(s)S(t)+D(S(s)-T(s))(S(t)-T(t)) with D ? B(X), solutions of H-generalized Cauchy equation are studied, where {T(t)}t?0 is a C-semigroup of operators. Also a similar equations are studied on C-cosine families and integrated C-semigroups.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim ◽  
Donal O’Regan ◽  
Adel A. Elmandouh
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Multivalued Function ◽  
Linear Operators ◽  
Solution Set ◽  
Cosine Family ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Noninstantaneous Impulses

AbstractIn this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

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