 About 115,000 results  books.google.com This book represents the first synthesis of the considerable body of new research into positive definite matrices. 

 books.google.com (b) Cc = (Ccαβ) is positive definite and weakly continuous; (c) C0 = (C0αβ) is
positive definite and each C0αβ is zero ... a weakly measurable unitary
representation (Uγ) γ∈Γ of Γ on L(G) and two bounded operators τα : Hα → G
such that Cαβ ... 

 books.google.com By finding an "integral representation," we mean the following: we are given a
certain positive definite function ii, : SS ... Also, we are interested in operator
valued positive definite functions and shall speak of "integral representations" (
via ... 

 books.google.com Not surprisingly, this correspondence will carry (completely) positive definite
maps on G to (completely) positive maps on C*(G). We begin by describing this
correspondence in one case of particular interest. Let Z" be the Cartesian product
of n ... 

 books.google.com This implies, by Hewitt and Ross [2,(32.8.b)] that the representation R, with all
operators R restricted to the closure of the ... f * f^, g = f and g = f~ * f. to see that
there is a positivedefinite operator B on (fo*r^) (fo"^} H(V ) commuting with all V
for ... 

 books.google.com As we mentioned before the above results appear as application of our results on
positive semidefinite completions. ... A complete Schur analysis of positive semi
definite operator matrices was given by T. Constantinescu in [7], and these ... 

 books.google.com Let H be a Hilbert space and let P be a linear operator in H (additive and
homogeneous but, possibly, unbounded) whose domain ... A symmetric operator
P is called positive definite if there exists a constant 72 > 0 such that (Pu,u) > 72
u2. 

 books.google.com Let us consider for simplicity the case of selfadjoint operator: G∗ = G. Then the
set of eigenvalues can be completely described in the case of positive definite
operator. DEFINITION. Let X = H be a Hilbert space. Then a linear continuous ... 

 books.google.com Therefore, we established that (L0, 0) > 0 for all 0 * 0 (c) and L is positivedefinite.
We prefer to write the operator in positivedefinite form for two reasons. First, if /,0
=/and L is a positivedefinite operator, then the weak solution (L$,v)(f,v) = Q ... 

 books.google.com In this chapter we are concerned with positive definite and semidefinite
completions of partial operator matrices, and we consider the banded case in
Section 2.1, the chordal case in Section 2.2, the Toeplitz case in Section 2.3, and
the ... 

 