TraceClass

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Contents

• The genuine trace-class Banach space
• Positive analytic trace in every basis
• Hilbert-Schmidt column synthesis
• Hilbert-Schmidt and trace-class compactness
• Entropy centers and one common reference
• Full-space thermal Hamiltonians
• Energy tightness and trace-norm compactness
• Extended entropy and real strong concavity
• A global entropy center before compactness
• Positive trace-class blocks
• Compression and discarded mass
• Finite-entropy relative entropy and a fixed reference
• Analytic trace in an arbitrary basis
• The actual trace-class product and ideal
• Hellinger energy and the trace norm
• Scalar square-sum Cauchy-Schwarz
• The two-sided trace-norm ideal estimate
• Zero spectral fibers and actual support
• Positive trace pairing and logarithmic regularization
• Ordered logarithmic energy
• The continuous observable trace pairing
• Actual polar factorization
• Trace-class positive-power series
• Fixed-block recorded quantum outputs
• Full spectrum and faithful finite or Nat reference bases
• Full spectral energy, self entropy and domination
• Cyclicity with a bounded factor