On Certain Densely Invariant Quantities of Linear Operators

✍ Scribed by R. W. Cross

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 639 KB
• Volume: 178
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19961780105

✦ Synopsis

Let L ( X ,

Y

) denote the class of linear transformations T : D ( T ) C X ---t Y where X and Y are normed spaces. A quantity f is called densely invariant if for every system L ( X , Y) and every operator T E L ( X , Y ) we have f ( T I E ) = f ( T ) whenever E is a core of T. The density invariance of certain well known quantities is established. In case Y is complete and T is closable, a stronger property is shown t o hold for some of these quantitites, namely invariance under restriction to dense subspaces.

If dimD(T) < 00, then all the quantities are zero. If dimD(T) = 00, then 1991 Mathematics Wbject Classification. Primary 47AO5.