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Introduction
Spectral Properties
Weighted Shifts
Weighted Shifts
Weighted Shifts
Powers and Direct Sums
John B Conway
George Washington University Washington, DC
Operator Theory and Related Topics Lille, May 31-June 3, 2010
Normal Operators
Introduction
Spectral Properties
Introduction
Weighted Shifts
Weighted Shifts
Weighted Shifts
Normal Operators
Joint work with Alejandro Rodriguez of Zayed University, Abu Dhabi
Introduction
Spectral Properties
Introduction
Weighted Shifts
Weighted Shifts
Weighted Shifts
Normal Operators
Joint work with Alejandro Rodriguez of Zayed University, Abu Dhabi TheproblemwassuggestedbyGabrielPrˇajituraˇ.
Introduction
Spectral Properties
Introduction
Weighted Shifts
Weighted Shifts
Weighted Shifts
Normal Operators
All Hilbert spaces are separable and complex. For any operatorAand 1n≤ ∞,A(n)denotes the direct sum ofAwith itselfntimes.
Introduction
Spectral Properties
Introduction
Weighted Shifts
Weighted Shifts
Weighted Shifts
Normal Operators
Say that an operatorAsatisfiesCondition SifA2is similar toA(2)=AA. Say thatAsatisfiesCondition UifA2is unitarily equivalent toAA.
Introduction
Spectral Properties
Introduction
Weighted Shifts
Weighted Shifts
Weighted Shifts
Normal Operators
Say that an operatorAsatisfiesCondition SifA2is similar toA(2)=AA. Say thatAsatisfiesCondition UifA2is unitarily equivalent toAA.
Why?
Introduction
Spectral Properties
Example The unilateral
Weighted Shifts
Weighted Shifts
Weighted Shifts
Normal Operators
shift and the bilateral shift satisfy Condition U.