Mayflower Hill 5830, Waterville ME 04901 Phone 207-859-5831 Fax 207-859-5846
Leo Livshits
Associate Professor of Mathematics
- Interests: My fields of research are Operator Theory and Linear Algebra. I am particularly interested in questions related to reducibility and transitivity of non-commutative operator semigroups, as well as in questions on Schur/Hadamard products of infinite matrices. For more information, see Leo's personal page.
- How to reach me:
- Office: Mudd 414
- Office phone: (207)-859-5844
- Email: llivshi AT colby DOT edu
- Postal address:
Leo Livshits Dept. of Mathematics Colby College Mayflower Hill 5830 Waterville, ME 04901
List of publications
(You need access to MathSciNet for most of the links below.)
MR2363973
Bernik, Janez; Drnov\v sek, Roman; Ko\v sir, Toma\v z; Livshits, Leo; Mastnak, Mitja; Omladi\v c, Matja\v z; Radjavi, Heydar Approximate permutability of traces on semigroups of matrices.
Oper. Matrices 1 (2007), no. 4, 455--467. 20M20 (15A30 15A42)
MR2327578
Livshits, Leo; MacDonald, Gordon; Radjavi, Heydar Topologically transitive matrix semigroups.
Oper. Matrices 1 (2007), no. 2, 165--179. (Reviewer: V. V. Peller) 47D03 (15A30 47A16)
MR2255476 (2007k:15025)
Semitransitivity Working Group at LAW'05 Semitransitive subspaces of matrices.
The Working Group was coordinated by Heydar Radjavi and its members
were: Janez Bernik, Roman Drnov\v sek, Don Hadwin, Ali Jafarian, Damjana Kokol
Bukov\v sek, Toma\v z Ko\v sir, Marjeta Kramar Fijav\v z, Thomas Laffey, Leo
Livshits, Mitja Mastnak, Roy Meshulam, Vladimir Müller, Eric Nordgren, Jan
Okni\'nski, Matja\v z Omladi\v c, Ahmed Sourour and Richard Timoney.
Electron. J. Linear Algebra 15 (2006), 225--238 (electronic). (Reviewer: Gordon Wilson MacDonald) 15A30 (47A15 47A16 47L05)
MR2110258 (2006b:47122)
Livshits, Leo; Ong, Sing-Cheong; Wang, Sheng-Wang Schur algebras over function algebras.
Houston J. Math. 30 (2004), no. 4, 1195--1217 (electronic). (Reviewer: Shijie Lu) 47L10 (46J10 46L99)
MR2073902 (2005c:20102)
Livshits, Leo On decomposability of periodic semigroups of non-negative
matrices.
Linear Algebra Appl. 383 (2004), 163--174. (Reviewer: K. S. S. Nambooripad) 20M20 (15A30)
MR2018595 (2004h:47009)
Livshits, L.; Macdonald, G.; Mathes, B.; Radjavi, H. Operator semigroups for which reducibility implies
decomposability.
Positivity 7 (2003), no. 3, 195--202. (Reviewer: Roman Drnov\v sek) 47A15 (47B65 47D03)
MR1987503 (2004c:15028)
Livshits, L.; MacDonald, G.; Mathes, B.; Okni\'nski, J.; Radjavi, H. Matrix semigroups with commutable rank.
Semigroup Forum 67 (2003), no. 2, 288--316. (Reviewer: Walter S. Sizer) 15A30 (15A03 47D03)
MR1885443 (2003j:47051)
Drnov\v sek, R.; Kokol-Bukov\v sek, D.; Livshits, L.; MacDonald, G.; Omladi\v c, M.; Radjavi, H. An irreducible semigroup of non-negative square-zero operators.
Integral Equations Operator Theory 42 (2002), no. 4, 449--460. (Reviewer: Douglas R. Farenick) 47D03 (47A15 47B38 47B65)
MR1897153 (2003m:47071)
Livshits, L.; MacDonald, G.; Mathes, B.; Radjavi, H. On band algebras.
J. Operator Theory 46 (2001), no. 3, suppl., 545--560. (Reviewer: Douglas R. Farenick) 47D03 (15A30 20M20 47A15 47L35)
MR1853675 (2002f:46087)
Livshits, Leo; Ong, S.-C.; Wang, S.-W. Banach space duality of absolute Schur algebras.
Integral Equations Operator Theory 41 (2001), no. 3, 343--359. (Reviewer: Shijie Lu) 46H35 (46A20 47B10 47L50)
MR1822227 (2002d:20102)
Livshits, Leo; MacDonald, Gordon $n$-transitivity and the complementation property.
Linear Algebra Appl. 329 (2001), no. 1-3, 157--169. (Reviewer: P. Rosenthal) 20M20 (15A30 47S10)
MR1784874 (2001e:20062)
Livshits, L.; Macdonald, G.; Radjavi, H. Cone-transitive matrix semigroups.
Linear and Multilinear Algebra 47 (2000), no. 4, 313--350. 20M20
MR1763047 (2001c:47045)
Drnov\v sek, Roman; Livshits, Leo; MacDonald, Gordon W.; Mathes, Ben; Radjavi, Heydar; \v Semrl, Peter On operator bands.
Studia Math. 139 (2000), no. 1, 91--100. 47D03 (47A15)
MR1733794 (2000i:20100)
Drnov\v sek, R.; Livshits, L.; MacDonald, G.; Mathes, B.; Radjavi, H.; \v Semrl, P. On transitive linear semigroups.
Linear Algebra Appl. 305 (2000), no. 1-3, 67--86. (Reviewer: K. D. Magill, Jr.) 20M20 (15A04 47A15 47D03)
MR1704128
Livshits, Leo Transitive linear semigroups.
The Second Meeting on Linear Algebra (Slovenian) (Bled, 1999).
Obzornik Mat. Fiz. 46 (1999), no. 2, 53--56. 15A04 (47D03)
MR1642522 (99m:47004)
Livshits, L.; MacDonald, G.; Mathes, B.; Radjavi, H. Reducible semigroups of idempotent operators.
J. Operator Theory 40 (1998), no. 1, 35--69. (Reviewer: Cecelia Laurie) 47A15 (20M99 47D03)
MR1361566 (96k:47061)
Livshits, Leo Continuity of Schur block-multiplication maps with respect to various
topologies.
J. Operator Theory 34 (1995), no. 1, 17--56. (Reviewer: Edward Azoff) 47B49 (47A05)
MR1332920 (96d:15040)
Livshits, Leo A note on $0$-$1$ Schur multipliers.
Linear Algebra Appl. 222 (1995), 15--22. (Reviewer: Sing Cheong Ong) 15A60
MR1310539 (96c:47007)
Livshits, Leo Block-matrix generalizations of infinite-dimensional Schur products and
Schur multipliers.
Linear and Multilinear Algebra 38 (1994), no. 1-2, 59--78. (Reviewer: T. Ando) 47A30 (15A60 46L05)
MR1208200 (94c:47055)
Livshits, Leonya; Ong, Sing-Cheong On the invertibility of the map $T\to STS\sp {-1}+S\sp {-1}TS$ and
operator-norm inequalities.
Linear Algebra Appl. 183 (1993), 117--129. (Reviewer: P. Rosenthal) 47B49 (15A09 47A30 47A62 47B15)
MR1159175 (93k:47054)
Livshits, Leonya Locally finite-dimensional sets of operators.
Proc. Amer. Math. Soc. 119 (1993), no. 1, 165--169. (Reviewer: Edward Azoff) 47D99 (47A99 47D15)