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We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
Reading the bibliography…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
Reading the bibliography…
O. Hanner, On the uniform convexity of L p L^{p} and l p l^{p}
1958
Earlier work this paper cites.
Z. Rubinstein, On a problem of Ilyeff
1968
Earlier work this paper cites.
N. Tomczak-Jaegermann, The moduli of smoothness and convexity and Rademacher averages of trace classes S p S_{p}
1974
Earlier work this paper cites.
K.V. Bhagwat and A. Subramanian, Inequalities between means of positive operators
1978
Earlier work this paper cites.
F. Kubo and T. Ando, Means of positive linear operators
1980
Earlier work this paper cites.
R.A. Horn and C. R. Johnson, Matrix Analysis
1985
Earlier work this paper cites.
R. Bhatia and F. Kittaneh, Norm inequalities for partitioned operators and an application
1990
Earlier work this paper cites.
D.S. Mitrinovic, J.E. Pecaric and A.M. Fink, Classical and New Inequalities in Analysis
1993
Earlier work this paper cites.
K. Ball, E. Carlen and E.H. Lieb, Sharp uniform convexity and smoothness inequalities for trace norms
1994
Earlier work this paper cites.
R. Bhatia, Matrix Analysis
1997
Earlier work this paper cites.
G. Schmeisser, The conjectures of Sendov and Smale
2002
Earlier work this paper cites.
C. King, Inequalities for trace norms of 2 × 2 2\times 2 block matrices
2003
Earlier work this paper cites.
R. Pereira, Differentiators and the geometry of polynomials
2003
Earlier work this paper cites.
R. Bhatia and F. Kittaneh, Clarkson inequalities with several operators
2004
Earlier work this paper cites.
C. King and M. Nathanson, New trace norm inequalities for 2 × 2 2\times 2 blocks of diagonal matrices
2004
Cited alongside, same era.
S.M. Malamud, Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
2005
Cited alongside, same era.
K.M.R. Audenaert, A norm compression inequality for block partitioned positive definite matrices
2006
Cited alongside, same era.
W.S. Cheung and T.W. Ng, A companion matrix approach to the study of zeros and critical points of a polynomial
2006
Cited alongside, same era.
T. Kosem, Inequalities between ‖ f ( A + B ) ‖ \left\|f(A+B)\right\| and ‖ f ( A ) + f ( B ) ‖ \left\|f(A)+f(B)\right\|
2006
Cited alongside, same era.
M. Uchiyama, Subadditivity of eigenvalue sums
2006
Cited alongside, same era.
K.M.R. Audenaert, A singular value for Heinz means
2007
Cited alongside, same era.
J.S. Aujla and J.-C. Bourin, Eigenvalue inequalities for convex and log-convex functions
2007
Cited alongside, same era.
J.-C. Bourin and M. Uchiyama, A matrix subadditivity inequality for f ( A + B ) f(A+B) and f ( A ) + f ( B ) f(A)+f(B)
2007
Cited alongside, same era.
S. Bravyi, Upper bounds on entangling rates of bipartite Hamiltonians
2007
Cited alongside, same era.
K.M.R. Audenaert, On a norm compression inequality for 2 × N 2\times N partitioned block matrices
2008
Cited alongside, same era.
K.M.R. Audenaert, On the Araki-Lieb-Thirring inequality
2008
Cited alongside, same era.
J.-C. Bourin, Matrix subadditivity inequalities and block-matrices
2009
Later among the works it cites.
J.-C. Bourin, A matrix subadditivity inequality for symmetric norms
2010
Later among the works it cites.
D. Wenzel and K.M.R. Audenaert, Impressions of convexity – An illustration for commutator bounds
2010
Later among the works it cites.
M. Crouzeix, Open problems on numerical range and functional calculus
2011
Later among the works it cites.
D. Khavinson, R. Pereira, M. Putinar, E.B. Saff and S. Shimoron, Borcea’s variance conjectures on the critical points of polynomials
2011
Later among the works it cites.
Weimin Miao, personal communication, 2011
2011
Later among the works it cites.
A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: theory of majorization and its applications
2011
Later among the works it cites.
2011
Later among the works it cites.
M. Adm and F. Kittaneh, Bounds and majorization relations for the critical points of polynomials
2012
Closest in time.
K.M.R. Audenaert, In-betweenness, a geometrical monotonicity property for operator means
2012
Closest in time.
K.M.R. Audenaert, Trace inequalities for completely monotone functions and Bernstein functions
2012
Closest in time.
J.-C. Bourin, T. Harada and E.-Y. Lee, Subadditivity inequalities for compact operators
2012
Closest in time.
E.-Y. Lee, How to compare the absolute values of operator sums and the sums of absolute values?
2012
Closest in time.
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