In this paper we provide a complete description of linear biseparating maps between spaces lip0（X^a, E） of Banach-valued little Lipschitz functions vanishing at infinity on locally com-pact HSlder metric spaces X^a=...In this paper we provide a complete description of linear biseparating maps between spaces lip0（X^a, E） of Banach-valued little Lipschitz functions vanishing at infinity on locally com-pact HSlder metric spaces X^a=（X,dx^a） with 0〈a〈1.Namely, it is proved that any linear bijection T ： lip0（X^a,E）→lip0（Y^a,F）satisfying that ｜｜Tf（y）｜｜F｜｜Tg（y）｜｜F= 0 for all y ∈ Y if and only if ｜｜f（x）｜｜E｜｜g（x）｜｜E=0 for all x E X, is a weighted composition operator of the form Tf（y） = h（y）（f（φ（y）））, where φ is a homeomorphism from Y onto X and h is a map from Y into the set of all linear bijections from E onto F. Moreover, T is continuous if and only if h（y） is continuous for all y ∈ Y. In this case, φ becomes a locally Lipschitz homeomorphism and h a locally Lipschitz map from Y^a into the space of all continuous linear bijections from E onto F with the metric induced by the operator canonical norm. This enables us to study the automatic continuity of T and the existence of discontinuous linear biseparating maps.展开更多
We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation spac...We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.展开更多
基金supported by Junta de Andalucia grants FQM-1438 and FQM-3737
文摘In this paper we provide a complete description of linear biseparating maps between spaces lip0（X^a, E） of Banach-valued little Lipschitz functions vanishing at infinity on locally com-pact HSlder metric spaces X^a=（X,dx^a） with 0〈a〈1.Namely, it is proved that any linear bijection T ： lip0（X^a,E）→lip0（Y^a,F）satisfying that ｜｜Tf（y）｜｜F｜｜Tg（y）｜｜F= 0 for all y ∈ Y if and only if ｜｜f（x）｜｜E｜｜g（x）｜｜E=0 for all x E X, is a weighted composition operator of the form Tf（y） = h（y）（f（φ（y）））, where φ is a homeomorphism from Y onto X and h is a map from Y into the set of all linear bijections from E onto F. Moreover, T is continuous if and only if h（y） is continuous for all y ∈ Y. In this case, φ becomes a locally Lipschitz homeomorphism and h a locally Lipschitz map from Y^a into the space of all continuous linear bijections from E onto F with the metric induced by the operator canonical norm. This enables us to study the automatic continuity of T and the existence of discontinuous linear biseparating maps.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M541899)the Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2013AQ021 and ZR2014AM002)+1 种基金National Natural Science Foundation of China(Grant Nos.11471190,11401414 and 11231005)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20140299)
文摘We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.
