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 .

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 an 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.

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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

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.
• 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

Telephone:

(803) 777-6190

Fax:

(803) 777-3783

Office

LeConte 300C