About 115,000 results
|This book represents the first synthesis of the considerable body of new research into positive definite matrices.|
|(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 ...
|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" (
|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 ...
|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 positive-definite operator B on (fo*r^) (fo"^} H(V ) commuting with all V
|As we mentioned before the above results appear as application of our results on |
positive semi-definite completions. ... A complete Schur analysis of positive semi-
definite operator matrices was given by T. Constantinescu in , and these ...
|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||
|Let us consider for simplicity the case of self-adjoint 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 ...
|Therefore, we established that (L0, 0) > 0 for all 0 * 0 (c) and L is positive-definite. |
We prefer to write the operator in positive-definite form for two reasons. First, if /,0
=/and L is a positive-definite operator, then the weak solution (L$,v)-(f,v) = Q ...
|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