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Let $$({\mathcal {M}},\tau )$$(M,τ) be a semi-finite von Neumann algebra, $$({\mathcal {N}},\tau |_{{\mathcal {N}}})$$(N,τ|N) be a semi-finite von Neumann subalgebra and $${\mathcal {E}}:\;{\mathcal {M}}\rightarrow {\mathcal {N}}$$E:M→N be a conditional expectation… Click to show full abstract
Let $$({\mathcal {M}},\tau )$$(M,τ) be a semi-finite von Neumann algebra, $$({\mathcal {N}},\tau |_{{\mathcal {N}}})$$(N,τ|N) be a semi-finite von Neumann subalgebra and $${\mathcal {E}}:\;{\mathcal {M}}\rightarrow {\mathcal {N}}$$E:M→N be a conditional expectation which leaves $$\tau $$τ invariant. We proved super-majorization for the conditional expectation $${\mathcal {E}}$$E and related inequalities.
Keywords:
conditional expectation;
property conditional;
expectation
Journal Title: Positivity
Year Published: 2018
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Journal Title: Positivity
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!