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• W2601554578 abstract "Let $f: mathbb{R}^d tomathbb{R}$ be a Lipschitz function. If $B$ is a bounded self-adjoint operator and if ${A_k}_{k=1}^d$ are commuting bounded self-adjoint operators such that $[A_k,B]in L_1(H),$ then $$|[f(A_1,cdots,A_d),B]|_{1,infty}leq c(d)|nabla(f)|_{infty}max_{1leq kleq d}|[A_k,B]|_1,$$ where $c(d)$ is a constant independent of $f$, $mathcal{M}$ and $A,B$ and $|cdot|_{1,infty}$ denotes the weak $L_1$-norm. If ${X_k}_{k=1}^d$ (respectively, ${Y_k}_{k=1}^d$) are commuting bounded self-adjoint operators such that $X_k-Y_kin L_1(H),$ then $$|f(X_1,cdots,X_d)-f(Y_1,cdots,Y_d)|_{1,infty}leq c(d)|nabla(f)|_{infty}max_{1leq kleq d}|X_k-Y_k|_1.$$" @default.
• W2601554578 created "2017-04-07" @default.
• W2601554578 creator A5019798517 @default.
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• W2601554578 date "2017-03-09" @default.
• W2601554578 modified "2023-09-27" @default.
• W2601554578 title "Weak type operator Lipschitz and commutator estimates for commuting tuples" @default.
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