# Publications

Forthcoming
Anoussis M, Katavolos A, Todorov IG.
Bimodules over vN(G), harmonic operators and  the non-commutative Poisson boundary
. Studia Mathematica. Forthcoming.Abstract
Starting with a left ideal J of L1(G) we consider its annihilator J ⊥ in L ∞ (G) and the generated VN(G)-bimodule in B(L 2 (G)), Bim(J ⊥ ). We prove that Bim(J ⊥ ) = (Ran J) ⊥ when G is weakly amenable discrete, compact or abelian, where Ran J is a suitable saturation of J in the trace class. We define jointly harmonic functions and jointly harmonic operators and show that, for these classes of groups, the space of jointly harmonic operators is the VN(G)-bimodule generated by the space of jointly harmonic functions. Using this, we give a proof of the following result of Izumi and Jaworski – Neufang: the non-commutative Poisson boundary is isomorphic to the crossed product of the space of harmonic functions by G.
2016
Anoussis M, Katavolos A, Todorov IG. Ideals of the {F}ourier algebra, supports and harmonic operators. Math. Proc. Cambridge Philos. Soc. [Internet]. 2016;161:223–235. Website
2015
Katavolos A. Operator algebras: an introduction. Serdica Math. J. 2015;41:49–82.
2014
Anoussis M, Katavolos A, Todorov IG. Ideals of {$A(G)$} and bimodules over maximal abelian selfadjoint algebras. J. Funct. Anal. [Internet]. 2014;266:6473–6500. Website
Katavolos A. Some operator algebras from semigroups. In: Algebraic methods in functional analysis. Vol. 233. Birkhäuser/Springer, Basel; 2014. pp. 75–84. Website
2012
Anoussis M, Katavolos A, Todorov IG. Operator algebras from the discrete {H}eisenberg semigroup. Proc. Edinb. Math. Soc. (2) [Internet]. 2012;55:1–22. Website
2011
Anoussis M, Katavolos A, Todorov IG. Angles in {$C^\ast$}-algebras. Houston J. Math. 2011;37:501–517.
2008
Introduction to Operator Theory (in Greek). Athens: Symmetria Publishers, Athens 2008; 2008.
2005
Katavolos A, Paulsen VI. On the ranges of bimodule projections. Canad. Math. Bull. [Internet]. 2005;48:97–111. Website
2003
Katavolos A, Todorov IG. Normalizers of operator algebras and reflexivity. Proc. London Math. Soc. (3) [Internet]. 2003;86:463–484. Website
2002
Katavolos A, Power SC. Translation and dilation invariant subspaces of {$L^2(\Bbb R)$}. J. Reine Angew. Math. [Internet]. 2002;552:101–129. Website
2001
Donsig AP, Katavolos A, Manoussos A. The {J}acobson radical for analytic crossed products. J. Funct. Anal. [Internet]. 2001;187:129–145. Website
Katavolos A, Lambrou MS, Longstaff WE. Pentagon subspace lattices on {B}anach spaces. J. Operator Theory. 2001;46:355–380.
1998
Katavolos A, Stamatopoulos C. Commutators of quasinilpotents and invariant subspaces. Studia Math. [Internet]. 1998;128:159–169. Website
Erdos JA, Katavolos A, Shulman VS. Rank one subspaces of bimodules over maximal abelian selfadjoint algebras. J. Funct. Anal. [Internet]. 1998;157:554–587. Website
1997
Katavolos A, Power SC. The {F}ourier binest algebra. Math. Proc. Cambridge Philos. Soc. [Internet]. 1997;122:525–539. Website
Katavolos A. Reflexivity, supports and spectral synthesis. In: Operator algebras and applications ({S}amos, 1996). Vol. 495. Kluwer Acad. Publ., Dordrecht; 1997. pp. 225–243.
Katavolos A. von Neumann algebras and unbounded operators (in Greek). In: Anoussis M, Kotsakis S, Hatzisavvas N Operator Algebras and Quantum Mechanics (Proceedings of the third Summer School in Analysis, Geometry and Mathematican Physics). Thessaloniki : Ziti Publishers; 1997.
1995
Barnes BA, Katavolos A. Corrigendum to: {P}roperties of quasinilpotents in some operator algebras'' [{P}roc. {R}oy. {I}rish {A}cad. {S}ect. {A} {\bf 93} (1993), no. 2, 155–170; {MR}1368821 (96j:47042)]. Proc. Roy. Irish Acad. Sect. A. 1995;95:249–250.
Anoussis M, Katavolos A. Isometries of {$C_p$}-spaces in nest algebras. J. London Math. Soc. (2) [Internet]. 1995;51:175–188. Website
Anoussis M, Katavolos A. Unitary actions on nests and the {W}eyl relations. Bull. London Math. Soc. [Internet]. 1995;27:265–272. Website
1993
Katavolos A, Lambrou MS, Longstaff WE. The decomposability of operators relative to two subspaces. Studia Math. [Internet]. 1993;105:25–36. Website
Barnes BA, Katavolos A. Properties of quasinilpotents in some operator algebras. Proc. Roy. Irish Acad. Sect. A. 1993;93:155–170.
Anoussis M, Katavolos A, Lambrou M. On the reflexive algebra with two invariant subspaces. J. Operator Theory. 1993;30:267–299.
Katavolos A, Lambrou MS, Papadakis M. On some algebras diagonalized by {$M$}-bases of {$l^2$}. Integral Equations Operator Theory [Internet]. 1993;17:68–94. Website
1991
Katavolos A. Decomposability of operators relative to two subspaces. In: Selfadjoint and nonselfadjoint operator algebras and operator theory ({F}ort {W}orth, {TX}, 1990). Vol. 120. Amer. Math. Soc., Providence, RI; 1991. pp. 77–81. Website
Katavolos A, Papanastassiou N. Order convergence in operator algebras. Math. Balkanica (N.S.). 1991;5:245–249.
1990
Katavolos A, Katsoulis E. Semisimplicity in operator algebras and subspace lattices. J. London Math. Soc. (2) [Internet]. 1990;42:365–372. Website
Katavolos A, Radjavi H. Simultaneous triangularization of operators on a {B}anach space. J. London Math. Soc. (2) [Internet]. 1990;41:547–554. Website
1987
Katavolos A, Strantzalos P. Introduction to the Theory of Differential Equations (in Greek). Athens: Kardamitsa Publishers; 1987.
1982
Katavolos A. Noncommutative {$L_{p}$}\ spaces. {II}. Canad. J. Math. [Internet]. 1982;34:1208–1214. Website
1981
Katavolos A. Are noncommutative {$L_{p}$}\ spaces really noncommutative?. Canad. J. Math. [Internet]. 1981;33:1319–1327. Website
1979
Katavolos A, Koch I. Extension of {T}omita-{T}akesaki theory to the unbounded algebra of the canonical commutation relations. Rep. Math. Phys. [Internet]. 1979;16:335–352. Website
1976
Katavolos A. Isometric mappings of non-commutative {$L_{p}$} spaces. Canad. J. Math. [Internet]. 1976;28:1180–1186. Website