List of publications
B V Rajarama Bhat.
(Last updated
on February 7, 2009)
(a) Preprints
A Problem of Powers and the Product of Spatial Product
Systems (with V. Liebscher and M. Skeide) Contribution to the proceedings of nthe 28th Quantum Probability
Confernece, Sep 2-8, 2007, in Guanajuato, Mexico
Maximal
Commutative Subalgebras Invariant for CP-Maps: (Counter-)Examples, (with Franco
Fagnola and Michael Skeide ). To appear in Infinite Dimensional Analysis,
Quantum Probability and Related Topics. arXiv:0804.1864
Subsystems of Fock Need
Not Be Fock: Spatial CP-Semigroups, (with Volkmar Liebscher and Michael Skeide
) arXiv:0804.2169.
(b) Books
Quantum Independent Processes I: From Classical
Probability to Quantum Stochastic Calculus (Springer Lecture Notes with D.
Applebaum, J. Kustermans, and J. M. Lindsay), (Ed. M. Schurmann and U. Franz),
Springer LNM 1865 (2005). MR2132092 (2005j:81087).
Lectures on
Operator Theory, (Editor jointly with G. Elliott and P. Fillmore), Fields
Institute for Research in Mathematical Sciences Monograph Series, Vol. 13,
Amer. Math. Soc. 323pp. (1999). MR 2001j:46077
Cocycles
of CCR flows, Memoirs of the American Mathematical Society, 149,
no. 709 (2001). MR 2002e:46083 Abstract
.ps-file
(107 pages)
(c) Thesis (under
the guidance of Prof. K. R. Parthasarathy)
Markov Dilations
of Nonconservative Quantum Dynamical Semigroups and a Quantum Boundary
Theory, submitted to Indian
Statistical Institute on July 6, 1993. Abstract
ps-file;
(101 pages)
(d) Published Papers
On a characterization of velocity maps in the space of
observables, Pacific Journal of Mathematics, Vol. 152, No.1 : 1-14 (1992); MR 92K:46099. Abstract
A stochastic differential
equation with time dependent and unbounded operator coefficients, (with Kalyan
B. Sinha). Journal
of Functional Analysis, Vol. 114, 12-31 (1993); MR 95a:60080.
Abstract
Generalized harmonic oscillators
in quantum probability, (with K.R. Parthasarathy), Seminaire de
Probabilites XXV, Springer LNM-1485
: 39-51 (1991); MR 93k:81117. Abstract
On greatest common
divisor matrices and their applications, Linear Algebra and Its
Applications,Vol. 158 : 77-99(1991) ; MR 92K:15038.
Abstract
On some convex sets and
their extreme points, (with V.Pati and V. S. Sunder), Mathematische Annalen,
296, 637-648 (1993); MR 94f:46076. Abstract
Kolmogorov's existence
theorem for Markov processes in C* algebras (with K. R. Parthasarathy),
Proceedings of Indian Academy of Sciences ( Math. Sci.), Vol.103, 253-262
(1994). MR 95g:46118. Abstract
Markov dilations of
nonconservative dynamical semigroups and a quantum boundary theory, (with K. R.
Parthasarathy) Annales de l'Institut Henri Poincare, Vol. 31, 601-651
(1995). MR 96i:46079. Abstract
Examples of unbounded
generators leading to nonconservative minimal semigroups, (with Kalyan B.
Sinha), Quantum Probability and Applications, Vol. IX, 89-103 (1994). Abstract
An index theory for quantum
dynamical semigroups, Transactions of American Mathematical Society, Vol. 348
561-583 (1996); MR 96g:46059. Abstract
Article
On quantum extensions of
semigroups of Brownian motions on an half-line (with F. Fagnola and K.B.
Sinha), Russian Journal of Mathematical Physics, (John Wiley) 4 (1),
13-28 (1996). MR 97j:81177. Abstract
On minimality of
Evans-Hudson flows (with F. Fagnola), Bull. dell' Unione Mat. Ital., Serie VII,
Vol. IX-A-3p. 671-683(1997). MR 98i:81124. Abstract
A generalised
intertwining lifting theorem, The Fields Institute Communications Volume 20:Operator
Algebras and their Applications, Vol. II, (Ed., P.A. Fillmore, J. A. Mingo), (
Amer. Math. Soc.), 1-10(1998). MR 99j:47010. Abstract
Product systems of one
dimensional Evans-Hudson flows, Quantum Probability Communications, Vol.
X (1998) 187-194. MR2001h:81127 Abstract
ps-file
(11 pages)
Minimal dilations of
quantum dynamical semigroups to semigroups of endomorphisms of C*-algebras,
Journal of the Ramanujan Mathematical Society 14, No. 2 (1999)109-124. MR2000m:46132. Abstract
ps-file
(15 pages)
Tensor product systems of
Hilbert modules and dilations of completely positive semigroups, (with M. Skeide), Infinite
Dimensional Analysis, Quantum Probability and Related Topics,
Vol. 3, Number 4, 519-575(2000). MR 2001m:46149 Abstract
ps-file
(68pages)
Minimal isometric
dilations of operator cocycles, the Journal of Integral Equations and
Operator Theory, Vol. 42 125-141 (2002).
Abstract
A model theory for $q$-commuting
contractive tuples, (with T. Bhattacharyya), the Journal of
Operator Theory, 47, Number 1, 97-116 (2002). Abstract
Atomic dilations, Advances in quantum dynamics (South
Hadley, MA, 2002), 99-107, Contemp. Math., 335, Amer. Math. Soc., Providence,
RI, 2003. MR 2026012
Standard noncommuting and commuting dilations of
commuting tuples. (with Tirthankar Bhattacharyya and Santanu Dey),
Trans. Amer. Math. Soc. 356 (2004), no.
4, 1551-1568. MR 2034318. Abstract
.ps
file math.OA/0204107
Type I product systems of Hilbert modules (with S. D. Barreto, V.
Liebscher and M. Skeide), J. Funct. Anal. 212 (2004),
no. 1, 121-181. MR 2065240. Abstract
.ps file
Regular quantum stochastic cocycles have exponential product
systems (with J. Martin Lindsay). in {\em Quantum Probability
and Infinite Dimensional Analysis,\/} Ed. M. Schurmann and U. Franz,
QP-PQ, Vol. XVIII, World Scientific
(2004) 126-140. MR2211885 (2007h:81128)
.pdf file (15 pages)
On product systems arising from sum systems (with R.
Srinivasan.), Infinite Dimensional Analysis,
Quantum Probability and Related Topics, Vol. 8, No. 1 (2005) 1-31.
.pdf
file (31 pages)
A completely entangled subspace of maximal dimension, International Journal of
Quantum Information, Vol. 4, No. 2 (2006) 325-330.
.pdf file (8 pages)
Minimal Cuntz-Krieger dilations and representations of
Cuntz-Krieger algebras. (with Santanu Dey and J. Zacharias), Proceedings of the Indian Academy
of Sciences, Mathematical Sciences, Vol. 116 (2006), No. 2,
193-220. MR2226131 (2007h:46066)
Integrators of
matrices, (with M. Mukherjee), Journal of Linear Algebra and its applications,
Vol. 426(2007), no.1, 71-82. MR2344560 (2008m:15014)
(e) Expository articles
Continuous tensor product
systems of Arveson and Powers’ Index Theory for E0-semigroups, Centro
Vito Volterra (Preprint series No. 177), Universita Degli Studi di Roma ”Tor
Vergata”, June 1994.
Dilations
of quantum Markov semigroups, in Symposium on Recent developments in E-semigroups
and related topics, Ritsumeikan University, Japan (2005).
Operators
as Random Variables, in Proceedings of the UGC sponsored national seminar on
spectral theory of operators and wavelet analysis, NSS College, Ottapalam,
45-51 (2006).