$[PHOTO]$
Anton R. Schep

As of January 1, 2021, I am retired as a Distinguished Professor Emeritus. I will continue refereeing papers for the foreseeable future, but only papers I can do a report on quickly or which interest me highly. On this page you can find links to information on classes I have taught and selected re- and preprints. To find information about our department, go to the Departmental homepage. For my professional background, see my curriculum vitae .

Research Interests

I am generally interested in the areas of Functional Analysis and Operator Theory. In particular my published research includes papers on:

the study of linear integral operators on Banach function spaces.
positive operators and C₀-semigroups of positive operators on Banach lattices.
spectral properties, and compactness properties of special classes of operators, such as disjointness preserving operators.

Publications

My Complete List of Publications (PDF file).

Click here to get a listing of my papers from the AMS MathSciNet with links to Mathematical Reviews.

Selected Reprints and Preprints (PDF Files)

The measure of non-compactness of a disjointness preserving operator
A slightly revised version appeared in: J. Operator Theory, 21(1989), 397-402.
And Still One More Proof of the Radon-Nikodym Theorem
Appeared in the Mathematical Monthly (2003). Here is an updated and improved version. UPDATE: When preparing a lecture for my graduate class, I decided that the second version was not as intuitive in its approach as the original version. Therefore I wrote a third version. much closer inspirit to the published version, but using ideas from the second version. Therefore check out this version too, if you plan to present the proof in a class.
Norms of positive operators on Lp-spaces
(with Ralph E. Howard), A revision appeared in: Proceedings of the American Mathematical Society,109 (1990), 135-146.
Lozanovskii's proof of Dunford's theorem
A rather loose translation of G. Ya. Lozanovskii's paper: N. Dunford's theorem, Izv. Vyss Ucebn. Zaved. Matem., 8(1974), 58-59 (in Russian).
Products of Cesaro convergent sequences with applications to convex solid sets and integral operators Proc. of the AMS 137 (2009), 579–584.
Products and Factors of Banach Function spaces Appeared in Positivity.
Minkowski’s integral inequality for function norms In this paper we give a necessary and sufficient condition on a pair of Fatou norms $\rho$ and $\lambda$ so that an inequality of the form $\rho(\lambda(f_x))\le C\lambda(\rho(f^y))$ holds for all nonnegative measurable functions $f(x, y)$. This paper appeared in Operator Theory in Function Spaces and Banach lattices, Operator Theory, Advances and Applications, vol. 75, Birkhauser, Basel–Boston–Berlin, 1995, pp. 299–308. Here we posted an updated version, which corrects an error in the published version.

Course materials

Fall 1998 Math 554/703I Syllabus
Spring 1999 Math 555/704I Syllabus
Fall 1999 Math 122 Syllabus
Fall 2000 Math 544
Spring 2001 Math 552/752I
Fall 2001 Math 703
Spring 2002 Math 704
Fall 2002 Math 544
Spring 2003 Math 544
Fall 2003 Math 554/Math 703I
Spring 2004 Math 555
Fall 2004 Math 300
Spring 2005 Math 554
Fall 2005 Math 703
Spring 2006 Math 704
Fall 2006 Math 554/Math 703I
Spring 2007 Math 555/704I
Fall 2007 Math 550
Spring 2008 Math 546
Fall 2008 Math 703
Spring 2009 Math 704
Fall 2009 Math 241
Spring 2010 Math 550
Fall 2010 Math 554/703I
Spring 2011 Math 555/704I
Fall 2011 Math 703
Spring 2012 Math 704
Fall 2012 Math 756
Spring 2013 Math 757
Spring 2014 Math 552
Fall 2014 Math 554/703I
Spring 2015 Math 241
Spring 2015 Math 704I
Fall 2015 Math 703
Spring 2016 Math 704
Fall 2016 Math 241
Spring 2017 Math 241
Fall 2017 Math 554/703I
Spring 2018 Math 555and704I
Spring 2019 Math 704
Fall 2019 Math 550
Spring 2020 Math 544
Fall 2020 Math 554/703I

Selected Notes (PDF Files)

Notes on Lebesgue's characterization of Riemann integrable functions
Weierstrass' original proof of the Weierstrass Approximation theorem.
A simple complex analysis and advanced calculus proof of the Fundamental Theorem of Algebra. The following version has appeared in The Mathematical Monthly.
Notes on the Riemann integral.
Notes on Complex analysis.
Notes on the Open Mapping theorem and related theorems.
A short proof of the Inverse Function Theorem.

How to reach me


Email:: schep AT math.sc.edu
Snail Mail:: Anton R. Schep
Department of Mathematics
University of South Carolina
Columbia, SC 29208
USA