Let C be a complex field, H_{m_1m_2} linear space of tensor products Hermite matrices H_{m_1}⊗H_{m_2} over , and suppose m_{1}, m_2≥2 are positive integers. A map f :H_{m_1m_2} → H_n is called inverse preserver if f( X_{1} ⊗X_{2} )^{-1}= X_{1}⊗X_{2}) ^{-1} ) for arbitrary invertible matrix ⊗ X_{2}∈ H_{m_{1}m_{2}} .The aim this...

The classification of preservers began about 100 years ago. In 1897, Frobenius characterized the linear operators on Mn which preserve certain matrix functions: those linear operators on Mn preserves the determinant and those preserves the characteristic polynomial (spectrum). He proved that if M M n n → : T is a linear transformation satisfying) det()) (T det(A A = , M A n ∈ , then either UAV ...

In this paper we investigate the structure of maps on classes of Hilbert space operators leaving the determinant of linear combinations invariant. Our main result is an infinite dimensional version of the famous theorem of Frobenius about determinant preserving linear maps on matrix algebras. In that theorem of ours, we use the notion of (Fredholm) determinant of bounded Hilbert space operators...

‎In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.

For nearly two decades, the amyloidhypothesis [22] has dominated the field of Alzheimer’s disease (AD) and during that time, massive efforts have focused on the role of amyloidin the pathogenesis of the disease. Given such focus, it is truly unfortunate that it is still unclear whether amyloidis either necessary or sufficient for the frank development of AD or whether amyloidcauses the associat...