Anton R. Schep

On this page you can find links to course information and
selected re- and preprints. To find information about our
department, go to the
Departmental homepage. For my
professional background, see my curriculum
vitae .

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 C
_{0}-semigroups of positive operators on Banach lattices. - spectral properties, and compactness properties of special classes of operators, such as disjointness preserving operators.

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

*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.

- 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

- 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.

*Email:*`schep AT math.sc.edu`*Snail Mail:*- Anton R. Schep

Department of Mathematics

University of South Carolina

Columbia, SC 29208

USA *Telephone:*- (803) 777-6190
*Fax:*- (803) 777-3783
*Office*- LeConte 317F