The PeriPersonal Space (PPS) has been defined as the space surrounding body, where physical interactions with elements of environment take place. As our world is social in nature, recent evidence revealed complex modulation factors onto PPS representation. In light growing interest field, this review we a close look at experimental approaches undertaken to assess impact Our also influences pers...

. In [2], the author has extended the above result for Bochner integrals of vectorvalued functions in real or complex Hilbert spaces. If (H ; 〈·, ·〉) is a Hilbert space over K (K = C,R) and f ∈ L ([a, b] ;H), this means that f : [a, b] → H is Bochner measurable on [a, b] and ∫ b a ‖f (t)‖ dt is finite, and there exists a constant K ≥ 1 and a vector e ∈ H, ‖e‖ = 1 such that (1.3) ‖f (t)‖ ≤ K Re ...

We give some ratio and difference reverses of the Cauchy–Schwarz inequality for complex functions of self-adjoint operators in Hilbert spaces, under suitable assumptions for the involved operators. Several examples for particular functions of interest are provided as well. Mathematics subject classification (2010): 47A63, 47A99.

The bilinear inequality is derived from the linear one with the help of an operatorvalued version of the Cauchy-Schwarz inequality. All these results, at least in their finite form, are obtained by simple and elegant methods well within the scope of a basic course on Hilbert spaces. (They can alternatively be obtained by tensor product techniques, but in the author’s view, these methods are les...

where φ : A → B(H) is a unital completely positive linear map from a C-algebra A to linear operators on a Hilbert space H, and x is a self-adjoint element in A with spectrum in I. Subsequently M. D. Choi [3] noted that it is enough to assume that φ is unital and positive. In fact, the restriction of φ to the commutative C-algebra generated by x is automatically completely positive by a theorem ...