16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.3.4

Operators on Inner Product Spaces

Mathematics — Linear Algebra · positive-operators-sum-product

Problem

Let

V

be a finite-dimensional inner product space. If

T

and

U

are positive linear operators on

V

, prove that

(T + U)

is positive. Give an example which shows that

TU

need not be positive.