NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF HOUSTON SYSTEM
Initial Amendment Date:	December 17, 1993
Latest Amendment Date:	December 4, 1995
Award Number:	9311487
Award Instrument:	Continuing Grant
Program Manager:	Bernard McDonald DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	December 15, 1993
End Date:	November 30, 1997 (Estimated)
Total Intended Award Amount:	$144,000.00
Total Awarded Amount to Date:	$144,000.00
Funds Obligated to Date:	FY 1994 = $48,000.00 FY 1995 = $48,000.00 FY 1996 = $48,000.00
History of Investigator:	Vern Paulsen (Principal Investigator) vern@math.uh.edu David Blecher (Co-Principal Investigator)
Recipient Sponsored Research Office:	University of Houston 4300 MARTIN LUTHER KING BLVD HOUSTON TX  US  77204-3067 (713)743-5773
Sponsor Congressional District:	18
Primary Place of Performance:	University of Houston 4300 MARTIN LUTHER KING BLVD HOUSTON TX  US  77204-3067
Primary Place of Performance Congressional District:	18
Unique Entity Identifier (UEI):	QKWEF8XLMTT3
Parent UEI:
NSF Program(s):	MODERN ANALYSIS, ANALYSIS PROGRAM
Primary Program Source:	app-0194  app-0195  app-0196
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	126200, 128100
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

9311487 Paulsen This project concerns three main lines of research. First, developing a Morita theory for operator algebras. This includes several stable isomorphism theorems and a deeper study of projective modules over operator algebras. Second, the project will examine operator space geometry and tensor products of operator spaces. Third, the project will conduct a study of analytic reproducing kernel Hilbert spaces. This research is in the general area of modern analysis and concerns the structure of spaces of operators or transformations. A fundamental problem in any area of mathematics is determining when two objects are equivalent and their geometry is similar. In this work, the investigators examine the families of transformations on a space and relate these transformations or operators to categories of structures through equivalences. The point is that theory known for one structure can often be shown to carry naturally to an equivalent structure. Thus, the approach is to demonstrate that rather complex families of operators have natural equivalences ***

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