Mayflower Hill 5830, Waterville ME 04901 Phone 207-859-5831 Fax 207-859-5846
Leo Livshits
Professor of Mathematics
Chair of Mathematics Department
- 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 another 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.)
MR2375070
Livshits, L.; MacDonald, G.; Marcoux, L. W.; Radjavi, H. A Kadison transitivity theorem for $C\sp *$-semigroups.
J. Funct. Anal. 254 (2008), no. 1, 246--266. 46Lxx (47Dxx)
MR2363973 (2008i:20074)
Bernik, Janez; Drnovšek, Roman; Košir, Tomaž; Livshits, Leo; Mastnak, Mitja; Omladič, Matjaž; Radjavi, Heydar Approximate permutability of traces on semigroups of matrices.
Oper. Matrices 1 (2007), no. 4, 455--467. (Reviewer: Wenxue Huang) 20M20 (15A30 15A42 47D03)
MR2327578 (2008e:47098)
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 Drnovšek, Don Hadwin, Ali Jafarian, Damjana Kokol
Bukovšek, Tomaž Košir, Marjeta Kramar Fijavž, Thomas Laffey, Leo
Livshits, Mitja Mastnak, Roy Meshulam, Vladimir Müller, Eric Nordgren, Jan
Okniński, Matjaž Omladič, 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 Drnovšek) 47A15 (47B65 47D03)
MR1987503 (2004c:15028)
Livshits, L.; MacDonald, G.; Mathes, B.; Okniński, 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)
Drnovšek, R.; Kokol-Bukovšek, D.; Livshits, L.; MacDonald, G.; Omladič, 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)
Drnovšek, Roman; Livshits, Leo; MacDonald, Gordon W.; Mathes, Ben; Radjavi, Heydar; Šemrl, Peter On operator bands.
Studia Math. 139 (2000), no. 1, 91--100. 47D03 (47A15)
MR1733794 (2000i:20100)
Drnovšek, R.; Livshits, L.; MacDonald, G.; Mathes, B.; Radjavi, H.; Šemrl, 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)
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