Joel Shapiro (mathematician)

Joel H. Shapiro is an American mathematician, active in the field of composition operators. He is the author of the book Composition Operators and Classical Function Theory (ISBN 3540940677), and the American Mathematical Society memoir "Cyclic Phenomena for Composition Operators" (Memoirs of the American Math. Society #596, Vol. 125, 1997, pp. 1–105), with Paul Bourdon.

Joel Shapiro
NationalityAmerican
Alma materCase Institute of Technology, University of Michigan
Known forFunctional analysis, Operator Theory, Composition Operators
Scientific career
FieldsMathematics
InstitutionsQueen's University, Canada, Michigan State University, Portland State University
Doctoral advisorAllen Shields
Doctoral studentsBarbara MacCluer

Career

Shapiro completed his PhD thesis entitled "Linear Functionals on Non-Locally Convex Spaces" under the supervision of Allen Shields in 1969 at the University of Michigan.[1] Upon graduating, he became a research associate at Queen's University, Canada, then from 1970 onwards was at Michigan State University, becoming a full professor in 1979. He stayed at Michigan until 2006, when he retired and became an adjunct professor at Portland State University in Oregon.

Shapiro discovered some of the properties of composition operators, including a study of the cyclic properties of such operators[2] and the first calculations of the essential norm [3] for composition operators on the Hardy spaces of the Unit disc.

gollark: It is not. Again, a isn't "the first thing" but "the x^2 thing".
gollark: That is also true but not what I mean here.
gollark: This is called commutativity.
gollark: It's entirely valid to reorder things you're adding together and the answer is the same.
gollark: You are too focused on the particular pattern of what you've done in class or whatever over the actual meaning.

References
  1. Joel Shapiro at the Mathematics Genealogy Project
  2. P. S. Bourdon and J. H. Shapiro, Mem. Amer. Math. Soc. 125 (1997), no. 596, pp. 1-105
  3. J. H. Shapiro, The essential norm of a composition operator. Ann. of Math. (2) 125 (1987), no. 2, 375–404.


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