Vol. 18, No. 1, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
An inequality for operators in a Hilbert space

Bertram Mond

Vol. 18 (1966), No. 1, 161–163
Abstract

Let A be a self-adjoint operator on a Hilbert space H satisfying mI A MI, 0 < m < M. Set q = M∕m. Let j and k be real numbers, jk0, j < k. Then

(Akx, x)1∕k∕(Ajx,x)1∕j
−1 j     −1∕k  −1 k     1∕j      − 1 k   j      (1∕k)−(1∕j)
≦ {j  (q  − 1)}   {k  (q − 1)}   {(k − j) (q − q )(x,x)}
for all x H(x0). Letting j = 1 and k = 1, this inequality reduces to (Ax,x)(A1x,x) [(M + m)24mM](x,x)2, the well-known Kantorovich Inequality.

Mathematical Subject Classification
Primary: 47.10
Secondary: 47.40
Milestones
Received: 11 March 1965
Published: 1 July 1966
Authors
Bertram Mond