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1

Deformation of involution and multiplication in a C*-algebra

100%

Najafi H., Moslehian M.

Studia Mathematica

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2013

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tom 215

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nr 1

31-37

EN

We investigate the deformations of involution and multiplication in a unital C*-algebra when its norm is fixed. Our main result is to present all multiplications and involutions on a given C*-algebra 𝓐 under which 𝓐 is still a C*-algebra when we keep the norm unchanged. For each invertible element a ∈ 𝓐 we also introduce an involution and a multiplication making 𝓐 into a C*-algebra in which a becomes a positive element. Further, we give a necessary and sufficient condition for the center of a unital C*-algebra 𝓐 to be trivial.

2

Operator entropy inequalities

81%

Moslehian M., Mirzapour F., Morassaei A.

Colloquium Mathematicum

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2013

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tom 130

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nr 2

159-168

EN

We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting $S_q^f(A|B): = ∑_{j=1}^{n} A_j^{1/2} (A_j^{-1/2}B_jA_j^{-1/2})^{q} f(A_j^{-1/2}B_jA_j^{-1/2})A_j^{1/2}$, and then give upper and lower bounds for $S_q^f(A|B)$ as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004), 219-235] under certain conditions. As an application, some inequalities concerning the classical Shannon entropy are deduced.

3

Moore-Penrose inverses of Gram operators on Hilbert C*-modules

81%

Moslehian M., Sharif K., Forough M., Chakoshi M.

Studia Mathematica

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2012

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tom 210

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nr 2

189-196

EN

Let t be a regular operator between Hilbert C*-modules and $t^{†}$ be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator t*t. More precisely, we study some conditions ensuring that $t^{†} = (t*t)^{†}t* = t*(tt*)^{†}$ and $(t*t)^{†} = t^{†}t*^{†}$. As an application, we get some results for densely defined closed operators on Hilbert C*-modules over C*-algebras of compact operators.

Ograniczanie wyników

2 Studia Mathematica

1 Colloquium Mathematicum

3 Moslehian M.

1 Chakoshi M.

1 Forough M.

1 Mirzapour F.

1 Morassaei A.

1 Najafi H.

1 Sharif K.

2 2013

1 2012

Deformation of involution and multiplication in a C*-algebra

Operator entropy inequalities

Moore-Penrose inverses of Gram operators on Hilbert C*-modules