Let mathcal{C}_p be the Schatten p -class for p>0 .

Generalizations of the parallelogram law for the Schatten 2 -norms have been given in the following form:

If mathbf{A}= {A_1,A_2, ldots,A_n } and mathbf{B}= {B_1,B_2...

We introduce the concept of the approximate Roberts orthogonality set and investigate the geometric properties of such sets. In addition, we introduce a notion of the approximate $a$-isosceles-orthogonality and consider ...

We introduce a notion of fuzzy Hilbert space and

establish a Cauchy--Schwarz type inequality. We also prove a

version of the parallelogram law in this setting. A fuzzy Hilbert

space theory can therefore be developed on this base....

A general operator parallelogram law

concerning a characterization of inner product spaces is established

and an operator extension of Bohr s inequality as well as several

norm inequalities are presented. More precisely, let...

We establish a general operator parallelogram law concerning a characterization of

inner product spaces, get an operator extension of Bohr’s inequality and present several norm

inequalities. More precisely, let A be a C...
A_t...
is integrable....