On a question of J. Borwein and H. Wiersma

Authors:
Boil Musev and Nadezhda Ribarska

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1707-1716

MSC (2010):
Primary 47H04, 52A41

DOI:
https://doi.org/10.1090/S0002-9939-2010-10602-0

Published electronically:
October 29, 2010

MathSciNet review:
2763759

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Abstract | References | Similar Articles | Additional Information

Abstract: We present an explicit example of an acyclic operator with bounded domain, thus answering a question of Borwein and Wiersma.

**1.**E. ASPLUND,*A monotone convergence theorem for sequences of nonlinear mappings*, Proc. Sympos. Pure Math., 18, Amer. Math. Soc., Providence, RI (1970), pp. 1-9. MR**0275240 (43:997)****2.**J.M. BORWEIN,*Maximal monotonicity via convex analysis*, J. Convex Anal., 13(2006), pp. 561-586. MR**2291552 (2008d:47096)****3.**J.M. BORWEIN, H. WIERSMA,*Asplund decomposition of monotone operators*, SIAM J. Optim., 18(2007), pp. 946-960. MR**2345978 (2009i:47107)****4.**R.T. ROCKAFELLAR,*Characterization of the subdifferentials of convex functions*, Pacific J. Math., 17(1966), pp. 497-510. MR**0193549 (33:1769)****5.**R.T. ROCKAFELLAR, R.J.-B. WETS,*Variational Analysis*, Springer, 2004. MR**1491362 (98m:49001)**

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Additional Information

**Boil Musev**

Affiliation:
Department of Mathematics and Informatics, University of Sofia, James Bourchier Boulevard 5, 1126 Sofia, Bulgaria – and – Institute of Mathematics and Informatics, BAS, G. Bonchev str. 8, 1113 Sofia, Bulgaria

Email:
boilbulgarian@gmail.com

**Nadezhda Ribarska**

Affiliation:
Department of Mathematics and Informatics, University of Sofia, James Bourchier Boulevard 5, 1126 Sofia, Bulgaria – and – Institute of Mathematics and Informatics, BAS, G. Bonchev str. 8, 1113 Sofia, Bulgaria

Email:
ribarska@fmi.uni-sofia.bg

DOI:
https://doi.org/10.1090/S0002-9939-2010-10602-0

Keywords:
Monotone operators,
cyclic monotonicity,
acyclic operators

Received by editor(s):
September 24, 2009

Received by editor(s) in revised form:
May 12, 2010, and May 20, 2010

Published electronically:
October 29, 2010

Additional Notes:
The first author was partially supported by the Bulgarian National Fund for Scientific Research under contract DO 02-360/2008

The second author was partially supported by the Bulgarian National Fund for Scientific Research under contract DO 02-360/2008

Communicated by:
Nigel J. Kalton

Article copyright:
© Copyright 2010
American Mathematical Society