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On extensions of orthosymmetric lattice bimorphisms

Mohamed Ali Toumi (2013)

Mathematica Bohemica

In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if ( A , * ) is a commutative d -algebra and A 𝔡 its Dedekind completion, then, A 𝔡 can be equipped...

On extremal positive maps acting between type I factors

Marcin Marciniak (2010)

Banach Center Publications

The paper is devoted to the problem of classification of extremal positive linear maps acting between 𝔅(𝒦) and 𝔅(ℋ) where 𝒦 and ℋ are Hilbert spaces. It is shown that every positive map with the property that rank ϕ(P) ≤ 1 for any one-dimensional projection P is a rank 1 preserver. This allows us to characterize all decomposable extremal maps as those which satisfy the above condition. Further, we prove that every extremal positive map which is 2-positive turns out to be automatically completely...

On generalized derivations in Banach algebras

Nadia Boudi, Said Ouchrif (2009)

Studia Mathematica

We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.

On group decompositions of bounded cosine sequences

Wojciech Chojnacki (2007)

Studia Mathematica

A two-sided sequence ( c ) n with values in a complex unital Banach algebra is a cosine sequence if it satisfies c n + m + c n - m = 2 c c for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence ( c ) n is bounded if s u p n | | c | | < . A (bounded) group decomposition for a cosine sequence c = ( c ) n is a representation of c as c = ( b + b - n ) / 2 for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying s u p n | | b | | < , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, here referred...

On homomorphisms between C * -algebras and linear derivations on C * -algebras

Chun-Gil Park, Hahng-Yun Chu, Won-Gil Park, Hee-Jeong Wee (2005)

Czechoslovak Mathematical Journal

It is shown that every almost linear Pexider mappings f , g , h from a unital C * -algebra 𝒜 into a unital C * -algebra are homomorphisms when f ( 2 n u y ) = f ( 2 n u ) f ( y ) , g ( 2 n u y ) = g ( 2 n u ) g ( y ) and h ( 2 n u y ) = h ( 2 n u ) h ( y ) hold for all unitaries u 𝒜 , all y 𝒜 , and all n , and that every almost linear continuous Pexider mappings f , g , h from a unital C * -algebra 𝒜 of real rank zero into a unital C * -algebra are homomorphisms when f ( 2 n u y ) = f ( 2 n u ) f ( y ) , g ( 2 n u y ) = g ( 2 n u ) g ( y ) and h ( 2 n u y ) = h ( 2 n u ) h ( y ) hold for all u { v 𝒜 v = v * and v is invertible } , all y 𝒜 and all n . Furthermore, we prove the Cauchy-Rassias stability of * -homomorphisms between unital C * -algebras, and -linear...

On hyponormal operators in Krein spaces

Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)

Archivum Mathematicum

In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators T for which there exists a fundamental decomposition 𝕂 = 𝕂 + 𝕂 - of the Krein space 𝕂 with 𝕂 + and 𝕂 - invariant under T .

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