Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Norms of positive operators on $ L\sp p$-spaces


Authors: Ralph Howard and Anton R. Schep
Journal: Proc. Amer. Math. Soc. 109 (1990), 135-146
MSC: Primary 47B38; Secondary 47A30
MathSciNet review: 1000156
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ 0 \leq T:{L^p}(Y,\nu ) \to {L^q}(X,\mu )$ be a positive linear operator and let $ \vert\vert T\vert{\vert _{p,q}}$ denote its operator norm. In this paper a method is given to compute $ \vert\vert T\vert{\vert _{p,q}}$ exactly or to bound $ \vert\vert T\vert{\vert _{p,q}}$ from above. As an application the exact norm $ \vert\vert V\vert{\vert _{p,q}}$ of the Volterra operator $ Vf(x) = \int_0^x {f(t)dt} $ is computed.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B38, 47A30

Retrieve articles in all journals with MSC: 47B38, 47A30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1000156-X
PII: S 0002-9939(1990)1000156-X
Keywords: Operator norms, positive linear operator, Volterra operator
Article copyright: © Copyright 1990 American Mathematical Society