TY - JOUR
AU - Hamburger, Hans Ludwig
AB - FIVE NOTES ON A GENERALIZATION OF QUASI-NILPOTENT TRANSFORMATIONS IN HILBERT SPACE By HANS LUDWIG HAMBURGER [Received 12 September 1950.—Read 12 October 1950] NOT E I On perfect N-transformations 1. GELFAND'S quasi-nilpotent transformations! suggest an interesting generalization. An account of investigations concerned with it will be given in a series of five successive Notes, the first and second of which deal with the simplest case only. The remaining Notes, in which some more general and more subtle types will be discussed, throw some light on the problem of the residual spectrum, a subject which has been neglected so far by mathematical research. To simplify our discussion we refer here to bounded linear transforma- tions in a Hilbert space £j; a great many of our considerations, however, may be also extended to reflexive Banach spaces. 2. Notations. If 91,33,... are any linear manifolds in §, we use the symbols 9(-f33> 9f © 33, and 910 93 in the same sense as in M. H. Stone's book.J We further write 9t n 93 for th e intersection of 9t and $8, 9t for the closure of 91, 91 for § G 91 which is closed, even if 91 is not closed. A 
TI - Five Notes on a Generalization of Quasi‐Nilpotent Transformations in Hilbert Space
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-1.1.494
DA - 1951-01-01
UR - https://www.deepdyve.com/lp/wiley/five-notes-on-a-generalization-of-quasi-nilpotent-transformations-in-1WJky0PzKX
SP - 494
EP - 512
VL - s3-1
IS - 1
DP - DeepDyve
ER -