shk | IIT Palakkad

Biosketch

Education

Ph. D. 1980 IIT Bombay

M. Sc. 1976 IIT Bombay

B. Sc. 1974 Pune University
Additional Information
Publications

Solution of an infinite band matrix equation.
Kulkarni, S. H.; Radha, R.; Sarvesh, K.
Banach Journal of Mathematical Analysis 17 (1) 14-28 (2023)
sarveshfinal.pdf (606.54 KB)

$G_1$-class elements in a Banach algebra
S. H. Kulkarni
The Journal of Analysis (2022)
G1-class.pdf (310.64 KB)

Condition pseudospectral radius of bounded linear operators
G. Krishna Kumar and S. H. Kulkarni
Linear Multilinear Algebra 70 (1) 27-41 (2022)

Spectrum and related sets: a survey
S. H. Kulkarni
Journal of Analysis 29 (2) 493-517 (2021)
spectrumsurvey.pdf (380.8 KB)

Operators that Attain Reduced Minimum
S. H. Kulkarni and G. Ramesh
Indian Journal of Pure and Applied Mathematics 51 (4) 1615-1631 (2021)
reducedmin-IJPAM-final.pdf (111.84 KB)

Gap formula for symmetric operators
S. H. Kulkarni and G. Ramesh
Proceedings of Telangana Academy of Sciences 1 (1) 129 - 133 (2020)

Shift invarant spaces in $L^2(\mathbb(R), \mathbb(C)^m)$ with $m$ generators
Anila John, S. H. Kulkarni and R. Radha
Journal of analysis 1-23 (2020)
anila1.pdf (598.34 KB)

Decomposition of the $(n. \epsilon)$-pseudospectrum of an element of a Banach algebra
Kousik Dhara and S. H. Kulkarni
Advances in Operator Theory 1-13 (2019)
Decomposition of the (n,eps)-pseudospectrum.pdf (437.45 KB)

Absolutely minimum attaining closed operators
S. H. Kulkarni and G. Ramesh
The Journal of Analysis 1-20 (2019)
SHKGR_AMclosed.pdf (526.33 KB)

Continuity of the $(n, \epsilon)$ Pseudospectrum in Banach Algebras
Kousik Dhara, S. H. Kulkarni and Markus Seidel
Integral Equations and Operator Theory 91 (32) 1-17 (2019)
Dhara2019_Article_ContinuityOfTheVarvecNEpsilonN.pdf (405.63 KB)

The $(n, \epsilon)$-pseudospectrum of an element of a Banach algebra
Kousik Dhara and S. H. Kulkarni
Jounal of Mathematical Analysis and Applicaions 464 939-954 (2018)
The (n,eps)-pseudospectrum of an element of a Banach algebra.pdf (402.99 KB)

Gelfand-Mazur Theorems in normed algebras: A survey
S. J. Bhatt and S. H. Kulkarni
Expositiones Mathematicae 36 166 - 177 (2018)
gelmazsurvey.pdf (249.99 KB)

Pseudospectra of elements of reduced Banach algebras II
Arundhathi Krishnan and S. H. Kulkarni
Functional Analysis, Approximation and Computation 10 (2) 33-45 (2018)
faac-10-2-4.pdf (272.5 KB)

On the denseness of minimum attaining operators
S. H. Kulkarni and G. Ramesh
Operators and Matrices 12 (3) 699-709 (2018)
oam-12-41-reprint-mindense.pdf (282.25 KB)

Pseudospectrum of an element of a Banach algebra
Arundhathi Krishnan and S. H. Kulkarni
Operators and Matrices 11 (1) 263-287 (2017)
oam-11-18-reprint.pdf (388.21 KB)

Pseudospectra of elements of reduced Banach algebras
Arundhathi Krishnan and S. H. Kulkarni
Advances in Operator Theory 2 (4) 475-493 (2017)
AOT_Volume 2_Issue 4_Pages 475-493.pdf (351.96 KB)

Banach algebra techniques to compute spectra, pseudospectra and condition spectra of some block operators with continuous symbols
G. Krishna Kumar and S. H. Kulkarni
Annals of Functional Analysis 6 (1) 148-169 (2015)
Banachalgebratecniques.pdf (7.67 MB)

The null space theorem
S. H. Kulkarni
Linear Algebra and its Applications 472 97-105 (2015)
nullspaceLAAfinal.pdf (271.31 KB)

Completeness and invertibility
S. H. Kulkarni
The Mathematics Student 84 (3-4) 141-145 (2015)
16-S H Kulkarni-ok.pdf (233.17 KB)

The group of invertible elements of a real Banach algebra
S. H. Kulkarni
Houston Journal of Mathematics 40 (3) (2014)
rbagrouphjm.pdf (257.04 KB)

Generalized inverses and approximation numbers
K. P. Deepesh, S. H. Kulkarni and M. T. Nair
Combinatorial matrix theory and generalized inverses of matrices 143-158 (2013)
Properties of Approximation numbers-Journal format.pdf (302.42 KB)

Approximation numbers for relatively bounded operators
K. P. Deepesh, S. H. Kulkarni and M. T. Nair
Functional Analysis, Approximation and Computation 5 (2) 35-42 (2013)
FAAC-appro-no-relatively-bounded.pdf (70.49 KB)

An Analogue of the Spectral Mapping Theorem for Condition Spectrum
G. Krishna Kumar and S. H. Kulkarni
Operator Theory: Advances and Applications 236 299-316 (2013)
21_Kumar-Kulkarni.pdf (6.22 MB)

Linear maps preserving pseudospectrum and condition spectrum
G. Krishna Kumar and S. H. Kulkarni
Banach Journal of Mathematical Analysis 6 (1) 45-60 (2012)
krishnakumar.bjma_.pdf (307.16 KB)

The carrier graph topology
S. H. Kulkarni and G. Ramesh
Banach Journal of Mathematical Analysis 5 (1) 56-69 (2011)
cgtbjma.pdf (305.21 KB)

Approximation of Moore-Penrose inverse of a closed operator by a sequence of finite rank outer inverses
S. H. Kulkarni and G. Ramesh
Functional Analysis, Approximation and Computation 3 (1) 23-32 (2011)
faac3-1-4.pdf (192.88 KB)

Error in "Wiener's theorem, infinite matrices and Banach algebras"
S. H. Kulkarni
Mathematics Newsletter 20 (3) 52 (2011)
errorwiener.pdf (79.68 KB)

Projection methods for computing Moore-Penrose inverses of unbounded operators
S. H. Kulkarni and G. Ramesh
Indian Journal of Pure and Applied Mathematics 41 (5) 647-662 (2010)
KILKARNI.pdf (159.67 KB)

Almost multiplicative functions on commutative Banach algebras
S. H. Kulkarni and D. Sukumar
Studia Mathematica 197 (1) 93-99 (2010)
sukumar3.pdf (182.81 KB)

A formula for gap between two closed operators
S. H. Kulkarni and G. Ramesh
Linear Algebra and its Applications 432 3912-3017 (2010)
LAA1Gap.pdf (266.66 KB)

Wiener's theorem, infinite matrices and Banach algebras
S. H. Kulkarni
Mathematics Newsletter 19 (2) 1-4 (2010)
nsmma09talk.pdf (148.67 KB)

Non-uniform sampling problem
S. H. Kulkarni, R. Radha and S. Sivananthan
Applied Functional Analysis 4 (1) 58-74 (2009)

Approximation numbers of operators on normed linear spaces
K. P. Deepesh, S. H. Kulkarni and M. T. Nair
Integral Equations and Operator Theory 65 (4) 529-542 (2009)
deepesh1.pdf (256.26 KB)

Projection methods for inversion of unbounded operators
S. H. Kulkarni and G. Ramesh
Indian Journal of Pure and Applied Mathematics 39 (2) 185-202 (2008)

The condition spectrum
S. H. Kulkarni and D. Sukumar
Acta Scientiarum Mathematicarum (Szeged) 74 (3-4) 625-641 (2008)
conspec1.pdf (296.62 KB)

Some properties of unbounded operators with closed range
S. H. Kulkarni, M. T. Nair and G. Ramesh
Proceedings of Indian Academy of Sciences (Mathematical Sciences) 118 (4) 613-625 (2008)
Kulkarni2008_Article_SomePropertiesOfUnboundedOpera.pdf (196.87 KB)

A relatively elementary proof of a characterization of polynomials
S. H. Kulkarni
Indian Journal of Pure and Applied Mathematics 38 (4) 229-230 (2007)
poly.pdf (105.26 KB)

An elementary proof for a characterization of *-isomorphisms
S. H. Kulkarni, M. T. Nair and M. N. N. Namboodiri
Proceedings of the American Mathematical Society 134 (1) 229-234 (2006)
stariso-pams.pdf (123.73 KB)

Solution of a tridiagonal operator equation
R. Balasubramanian, S. H. Kulkarni and R. Radha
Linear Algebra and its Applications 414 (1) 389-405 (2006)
tridiagonal-laa.pdf (187.74 KB)

Gleason-Kahane-Zelazko theorem for spectrally bounded algebra
S. H. Kulkarni and D. Sukumar
International Journal of Mathematics and Mathematical Sciences 15 2447-2460 (2005)
GKZspectral.pdf (943.48 KB)

A very simple and elementary proof of a theorem of Ingelstam
S. H. Kulkarni
American Mathematical Monthly 111 (1) 54-58 (2004)
ingel.pdf (84.3 KB)

Spectral theorem for an unbounded normal operator in a real Hilbert space
Sushama Agrawal and S. H. Kulkarni
Journal of analysis 12 107-114 (2004)

Three types of operator monotonocity
S. H. Kulkarni and K. C. Sivakumar
Journal of analysis 12 153-163 (2004)
kcsmono.pdf (151.69 KB)

Finite dimensional approximations of operator equations
R. Balasubramanian, S. H. Kulkarni and R. Radha
Linear algebra, numerical functional analysis and wavelet analysis 57-64 (2003)
finite.pdf (60.63 KB)

Spectral isometries of real commutative Banach algebras
Sushama Agrawal and S. H. Kulkarni
Real Analysis Exchange 167-172 (2002)
SUSPAP.pdf (222.1 KB)

Non-invertibility of certain almost Mathieu operators
R. Balasubramanian, S. H. Kulkarni and R. Radha
Proceedings of the American Mathematical Society 129 (7) 2017-2018 (2001)
almostmathieu.pdf (87.52 KB)

Spectral representation of a quaternionic Hilbert space
Sushama Agrawal and S. H. Kulkarni
Mathematics Today 19 (1) 3-8 (2001)
quaternion.pdf (7.85 MB)

Boundaries and Choquet sets for real subspaces of C(X)
S. H. Kulkarni and B. V. Limaye
Mathematica Japonica 51 (2) 199-212 (2000)

A characterization of closed range operators
S. H. Kulkarni and M. T. Nair
Indian Journal of Pure and Applied Mathematics 31 (4) 353-361 (2000)

Arzela-Ascoli theorem is stable
S. H. Kulkarni
International Journal of Mathematics Education in Science and Technology 31 (6) 919-922 (2000)
arzelastable.pdf (117.23 KB)

Dual spaces of quaternion normed linear spaces and reflexivity
Sushama Agrawal and S. H. Kulkarni
Journal of analysis 8 79-90 (2000)

An analogue of the Riesz representation theorem
Sushama Agrawal and S. H. Kulkarni
Novi Sad Journal of Mathematics 30 (1) 143-154 (2000)
NSJOM_30_1_143_154.pdf (147 KB)

A note on the Gelfand-Mazur theorem
S. J. Bhatt, D. J. Karia, S. H. Kulkarni and M. E. Shimpi
Proceedings of the American Mathematical Society 126 (10) 2999-3005 (1998)
GelfandMazurPAMS.pdf (196.56 KB)

Some applications of a spectral theorem for normal operators on a real Hilbert space
Sushama Agrawal and S. H. Kulkarni
Mathematics Today 16 65-76 (1998)

Explicit solutions of a special class of linear programming problems in Banach spaces
S. H. Kulkarni and K. C. Sivakumar
Acta Scientiarum Mathematicarum (Szeged) 62 457-465 (1996)

Applications of generalized inverses to interval linear programs in Hilbert spaces
S. H. Kulkarni and K. C. Sivakumar
Numerical Functional Analysis and Optimization 16 (7-8) 965-973 (1995)