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

I use the PDF format for my more technical documents. Click to obtain a free copy of Acrobat Reader to view PDF files.

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. (Note: You or your institution must have a valid MathSciNet subscription.)

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.
• 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 To appear 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

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 will appear 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