Fréchet differentiability of the norm of $L_p$-spaces associated with arbitrary von Neumann algebras

DOI10.1090/tran/7215zbMath1426.46043OpenAlexW2592390318MaRDI QIDQ5380474

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Publication date: 5 June 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/7215

zbMATH Keywords

differentiability of the normsingular traceHaagerup \( L_p\)-space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Noncommutative function spaces (46L52) Derivatives of functions in infinite-dimensional spaces (46G05)

Cites Work

• Spectral shift function of higher order
• Singular traces. Theory and applications
• Functions of operators under perturbations of class \(S_p\)
• Applications of the complex interpolation method to a von Neumann algebra: non-commutative \(L^ p\)-spaces
• Double operator integrals
• Sums of commutators in ideals and modules of type II factors.
• Generalized s-numbers of \(\tau\)-measurable operators
• Positive cones and \(L^p\)-spaces for von Neumann algebras
• Differentiation of operator functions in non-commutative \(L_{p}\)-spaces
• Singular traces on semifinite von Neumann algebras
• Fréchet differentiability of \(\mathcal{S}^p\) norms
• Multiple operator integrals and higher operator derivatives
• Smooth Banach spaces
• Derivations in algebras of operator-valued functions
• Symmetric norms and spaces of operators
• Operator Integrals, Spectral Shift, and Spectral Flow
• Applications of Uniform Convexity of Noncommutative L p -Spaces
• Contractive projections in 𝐶_{𝑝}
• Local uniform and uniform convexity of non-commutative symmetric spaces of measurable operators
• Rigid $\mathcal{OL}_p$structures of non-commutative $L_p$-spaces associated with hyperfinite von Neumann algebras
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