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The Maslov Index in Symplectic Banach Spaces
 
Bernhelm Booß-Bavnbek Roskilde University, Roskilde, Denmark
Chaofeng Zhu Nankai University, Tianjin, People’s Republic of China
The Maslov Index in Symplectic Banach Spaces
Softcover ISBN:  978-1-4704-2800-6
Product Code:  MEMO/252/1201
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4371-9
Product Code:  MEMO/252/1201.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2800-6
eBook: ISBN:  978-1-4704-4371-9
Product Code:  MEMO/252/1201.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
The Maslov Index in Symplectic Banach Spaces
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The Maslov Index in Symplectic Banach Spaces
Bernhelm Booß-Bavnbek Roskilde University, Roskilde, Denmark
Chaofeng Zhu Nankai University, Tianjin, People’s Republic of China
Softcover ISBN:  978-1-4704-2800-6
Product Code:  MEMO/252/1201
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4371-9
Product Code:  MEMO/252/1201.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2800-6
eBook ISBN:  978-1-4704-4371-9
Product Code:  MEMO/252/1201.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2522018; 123 pp
    MSC: Primary 53; Secondary 58

    The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index.

    As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

  • Table of Contents
     
     
    • Chapters
    • Preface
    • Introduction
    • 1. Maslov index in symplectic Banach spaces
    • 1. General theory of symplectic analysis in Banach spaces
    • 2. The Maslov index in strong symplectic Hilbert space
    • 3. The Maslov index in Banach bundles over a closed interval
    • 2. Applications in global analysis
    • 4. The desuspension spectral flow formula
    • A. Perturbation of closed subspaces in Banach spaces
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2522018; 123 pp
MSC: Primary 53; Secondary 58

The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index.

As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

  • Chapters
  • Preface
  • Introduction
  • 1. Maslov index in symplectic Banach spaces
  • 1. General theory of symplectic analysis in Banach spaces
  • 2. The Maslov index in strong symplectic Hilbert space
  • 3. The Maslov index in Banach bundles over a closed interval
  • 2. Applications in global analysis
  • 4. The desuspension spectral flow formula
  • A. Perturbation of closed subspaces in Banach spaces
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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