最新公告
  • 欢迎您光临IO源码网,本站秉承服务宗旨 履行“站长”责任,销售只是起点 服务永无止境!立即加入我们
  • Grothendieck Spaces The Landscape and Perspectives PDF 下载

    Grothendieck Spaces  The Landscape and Perspectives PDF 下载

    本站整理下载:
    链接:https://pan.baidu.com/s/14yUQxqs-JhXs6gtT5LD7Ww 
    提取码:kj4m 
    相关截图:
    主要内容:

    2.1. L p -spaces and related concepts
    Let 1 6 λ < ∞ and 1 6 p 6 ∞. A Banach space X is a L p,λ -space whenever every
    finite-dimensional subspace F of X is contained in another finite-dimensional space G of
    X whose Banach–Mazur distance to ‘ dimG
    p
    is at most λ. A Banach space X is said to be a
    L p -space if it is a L p,λ -space for some λ. We will be primarily interested in the L ∞ -spaces
    and the L 1 -spaces. A Banach space X is a Lindenstrauss space, whenever it is a L ∞,λ -space
    for every λ > 1; equivalently, if X is an isometric predual of some L 1 (µ)-space. Spaces of
    the form C 0 (K) for some locally compact space K are natural examples of Lindenstrauss
    spaces.
    We say that a Banach space X is a
    g
    OL ∞,λ -space whenever every finite-dimensional
    subspace of X is contained in another finite-dimensional subspace whose Banach–Mazur
    distance to some finite-dimensional C ∗ -algebra is at most λ. The g OL ∞ -spaces are the space
    which are
    g
    OL λ,∞ -spaces for some λ > 1.
    The just-introduced terminology concerning
    g
    OL ∞ -spaces is not standard as the non-
    commutative analogues of L ∞,λ -spaces—usually termed OL ∞,λ -spaces—are defined in terms
    of the completely bounded Banach–Mazur distance to the set of finite-dimensional C ∗ –
    algebras. OL ∞,λ are
    g
    OL ∞,λ -spaces. A C ∗ -algebra is nuclear if and only if it is OL ∞,λ for
    some λ > 6 ([83, Theorem 1.2]). We refer to [83] for additional information and a more
    precise definition of these spaces.
    2.2. Direct sums and ultraproducts
    Let Γ be a (possibly uncountable) set and let E be a Banach space that has a normalised,
    1-unconditional basis (e γ ) γ∈Γ . Given a collection (X γ ) γ∈Γ of Banach spaces, the E-sum of
    (X γ ) γ∈Γ , denoted by ( L γ∈Γ X γ ) E , is the set of all tuples (x γ ) γ∈Γ with x γ ∈ X γ for each
    6 M. GONZÁLEZ AND T. KANIA
    γ ∈ Γ, and such that
    P
    γ∈Γ kx γ ke γ
    ∈ E. Formally, the E-sum depends on the choice of the
    basis but when the basis is clear from the context we can afford this abuse of notation.
    If the basis (e γ ) γ∈Γ is shrinking, the coordinate functionals (e ∗
    γ ) γ∈Γ
    associated to that
    basis form a normalised, 1-unconditional basis of E ∗ . In this case, the map
    Λ E : (
    M
    γ∈Γ
    X ∗
    γ ) E ∗
    ?
    (
    M
    γ∈Γ
    X γ ) E
    ? ∗
    given by
    ? (x
    γ ) γ∈Γ ,Λ E (f γ ) γ∈Γ
    ?
    =
    X
    γ∈Γ
    hx γ ,f γ i
    for (x γ ) γ∈Γ ∈ ( L γ∈Γ X γ ) E and (f γ ) γ∈Γ ∈ ( L γ∈Γ X ∗
    γ ) E ∗ , is an isometric isomorphism (see
    [104, Section 4] for details). When the basis (e γ ) γ∈Γ is additionally boundedly complete
    (which implies that E is reflexive), the bidual of ( L γ∈Γ X γ ) E is naturally isometrically
    isomorphic to ( L γ∈Γ X ∗∗
    γ
    ) E .
    Let Γ be an infinite set and let {X γ : γ ∈ Γ} be a family of Banach spaces. The ‘ ∞ -sum
    of (X γ ) γ∈Γ , denoted ( L γ∈Γ X γ ) ‘ ∞ (Γ) , is the set of all tuples (x γ ) i∈Γ such that x γ ∈ X γ
    (γ ∈ Γ) and k(x γ ) γ∈Γ k ‘ ∞ (Γ) = sup γ∈Γ kx γ k < ∞; it is a Banach space with respect to this
    norm. When X γ = Z for each γ ∈ Γ, we write X = ‘ ∞ (Γ,Z).
    Let U be a non-trivial ultrafilter on Γ (assuming that Γ is infinite). Then
    N U ? (X γ ) γ∈Γ ? =
    ? (x
    γ ) γ∈Γ ∈ E: lim
    γ→U
    kx γ k = 0 ?
    is a closed subspace of X := ( L γ∈Γ X γ ) E . The ultraproduct of {X γ : γ ∈ Γ} along U,
    denoted [X γ ] U , is defined as the quotient space X/N U ((X γ ) γ∈Γ ); when X γ = Z for all
    γ ∈ Γ, then we call the quotient space an ultrapower of Z (along U).
    2.3. Ordered normed spaces
    Let E be a normed space. A convex subset P ⊂ E is a cone, whenever λP = P for
    all λ > 0 and P ∩ (−P) = {0}. An ordered normed space is a normed space E with a
    distinguished cone P; we will denote by (E,P) an ordered normed space or simply by E
    if the choice of the cone is clear from the context.
    For x,y ∈ E we write x 6 y as long as y − x ∈ P. If there exists a number λ > 0
    such that whenever 0 6 x 6 y (x,y ∈ E) we have kxk 6 λkyk, the cone P is called
    normal. An order unit of (E,P) is an element e ∈ P such that for every x ∈ P there
    is some n ∈ N with x 6 n · e. A convex subset B of P is called a base for P, whenever
    for each non-zero x ∈ P there is a unique real number f(x) > 0 such that f(x) −1 x ∈ B.
    A cone P is well-based in X if it has a bounded base B defined by a some f ∈ X ∗ , that
    is, B = {x ∈ P : hf,xi = 1}. An element x ∈ P is a quasi-interior point of P, when the
    order interval [0,x] = {z ∈ E: 0 6 z 6 x} is linearly dense in X. Whenever E is a Banach
    lattice or a C ∗ -algebra, by default we consider the (canonical) positive cone E + therein.
    Definition 2.3.1. Let (E,P) be an ordered normed space.

     

    *** 次数:10600 已用完,请联系开发者***

    1. 本站所有资源来源于用户上传和网络,因此不包含技术服务请大家谅解!如有侵权请邮件联系客服!384324621@qq.com
    2. 本站不保证所提供下载的资源的准确性、安全性和完整性,资源仅供下载学习之用!如有链接无法下载、失效或广告,请联系客服处理,有奖励!
    3. 您必须在下载后的24个小时之内,从您的电脑中彻底删除上述内容资源!如用于商业或者非法用途,与本站无关,一切后果请用户自负!
    4. 如果您也有好的资源或教程,您可以投稿发布,成功分享后有★币奖励和额外收入!

    IO 源码网 » Grothendieck Spaces The Landscape and Perspectives PDF 下载

    常见问题FAQ

    免费下载或者VIP会员专享资源能否直接商用?
    本站所有资源版权均属于原作者所有,这里所提供资源均只能用于参考学习用,请勿直接商用。若由于商用引起版权纠纷,一切责任均由使用者承担。更多说明请参考 VIP介绍。
    提示下载完但解压或打开不了?
    最常见的情况是下载不完整: 可对比下载完压缩包的与网盘上的容量,若小于网盘提示的容量则是这个原因。这是浏览器下载的bug,建议用百度网盘软件或迅雷下载。若排除这种情况,可在对应资源底部留言,或 联络我们.。
    找不到素材资源介绍文章里的示例图片?
    对于PPT,KEY,Mockups,APP,网页模版等类型的素材,文章内用于介绍的图片通常并不包含在对应可供下载素材包内。这些相关商业图片需另外购买,且本站不负责(也没有办法)找到出处。 同样地一些字体文件也是这种情况,但部分素材会在素材包内有一份字体下载链接清单。
    IO源码吧
    一个高级程序员模板开发平台

    发表评论

    • 177会员总数(位)
    • 12330资源总数(个)
    • 53本周发布(个)
    • 0 今日发布(个)
    • 563稳定运行(天)

    提供最优质的资源集合

    立即查看 了解详情