Fréchet differentiability of the norm of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>-spaces associated with arbitrary von Neumann algebras
Tài liệu tham khảo
Azamov, 2009, Operator integrals, spectral shift, and spectral flow, Can. J. Math., 61, 241, 10.4153/CJM-2009-012-0
Birman, 1966, Double Stieltjes operator integrals, 33
Birman, 1967, Double Stieltjes operator integrals II, vol. 2, 26
Birman, 1973, Double Stieltjes operator integrals III, vol. 6, 27
Bonic, 1966, Smooth functions on Banach manifolds, J. Math. Mech., 15, 877
de Pagter, 2004, Differentiation of operator functions in non-commutative Lp-spaces, J. Funct. Anal., 212, 28, 10.1016/j.jfa.2003.10.009
de Pagter, 2002, Double operator integrals, J. Funct. Anal., 192, 52, 10.1006/jfan.2001.3898
Fack, 1986, Generalized s-numbers of τ-measurable operators, Pac. J. Math., 123, 269, 10.2140/pjm.1986.123.269
Haagerup, 1977, Lp-spaces associated with an arbitrary von Neumann algebra, 175
Kadison, 1986, Fundamentals of the Theory of Operator Algebras, vol. II. Advanced Theory, vol. 100
Lord, 2012, Singular Traces: Theory and Applications, vol. 46
Lusternik, 1961
Peller, 2006, Multiple operator integrals and higher operator derivatives, J. Funct. Anal., 233, 515, 10.1016/j.jfa.2005.09.003
Pisier, 2003, Non-commutative Lp-Spaces, vol. 2, 1459
Potapov, 2014, Fréchet differentiability of Sp norms, Adv. Math., 262, 436, 10.1016/j.aim.2014.05.011
Potapov, 2013, Spectral shift function of higher order, Invent. Math., 193, 501, 10.1007/s00222-012-0431-2
Sundaresan, 1967, Smooth Banach spaces, Math. Ann., 173, 191, 10.1007/BF01361710
Terp, 1981
Thiago Bernardino, 2009, A simple natural approach to the Uniform Boundedness Principle for multilinear mappings, Proyecciones, 28, 203
Tomczak-Jaegermann, 1975, On the differentiability of the norm in trace classes Sp