Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Methods in the Theory of Hereditarily Indecomposable Banach Spaces
 
Spiros A. Argyros National Technical University of Athens, Athens, Greece
Andreas Tolias National Technical University of Athens, Athens, Greece
Methods in the Theory of Hereditarily Indecomposable Banach Spaces
eBook ISBN:  978-1-4704-0407-9
Product Code:  MEMO/170/806.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
Methods in the Theory of Hereditarily Indecomposable Banach Spaces
Click above image for expanded view
Methods in the Theory of Hereditarily Indecomposable Banach Spaces
Spiros A. Argyros National Technical University of Athens, Athens, Greece
Andreas Tolias National Technical University of Athens, Athens, Greece
eBook ISBN:  978-1-4704-0407-9
Product Code:  MEMO/170/806.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1702004; 114 pp
    MSC: Primary 46;

    A general method producing Hereditarily Indecomposable (H.I.) Banach spaces is provided. We apply this method to construct a nonseparable H.I. Banach space \(Y\). This space is the dual, as well as the second dual, of a separable H.I. Banach space. Moreover the space of bounded linear operators \({\mathcal{L}}Y\) consists of elements of the form \(\lambda I+W\) where \(W\) is a weakly compact operator and hence it has separable range. Another consequence of the exhibited method is the proof of the complete dichotomy for quotients of H.I. Banach spaces. Namely we show that every separable Banach space \(Z\) not containing an isomorphic copy of \(\ell^1\) is a quotient of a separable H.I. space \(X\). Furthermore the isomorph of \(Z^*\) into \(X^*\), defined by the conjugate operator of the quotient map, is a complemented subspace of \(X^*\).

    Readership

    Graduate students and research mathematicians interested in analysis.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. General results about H.I. spaces
    • 2. Schreier families and repeated averages
    • 3. The space $X = T[G, (\mathcal {S}_{n_j}, 1/m_j)_j, D]$ and the auxiliary space $T_{ad}$
    • 4. The basic inequality
    • 5. Special convex combinations in $X$
    • 6. Rapidly increasing sequences
    • 7. Defining $D$ to obtain a H.I. space $X_G$
    • 8. The predual $(X_G)_*$ of $X_G$ is also H.I.
    • 9. The structure of the space of operators $\mathcal {L}(X_G)$
    • 10. Defining $G$ to obtain a nonseparable H.I. space $X^*_G$
    • 11. Complemented embedding of $l^p$, $1 \leq p < \infty $, in the duals of H.I. spaces
    • 12. Compact families in $\mathbb {N}$
    • 13. The space $X_G = T[G, (\mathcal {S}_\xi , 1/m_j)_j, D]$ for an $\mathcal {S}_\xi $ bounded set $G$
    • 14. Quotients of H.I. spaces
  • 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: 1702004; 114 pp
MSC: Primary 46;

A general method producing Hereditarily Indecomposable (H.I.) Banach spaces is provided. We apply this method to construct a nonseparable H.I. Banach space \(Y\). This space is the dual, as well as the second dual, of a separable H.I. Banach space. Moreover the space of bounded linear operators \({\mathcal{L}}Y\) consists of elements of the form \(\lambda I+W\) where \(W\) is a weakly compact operator and hence it has separable range. Another consequence of the exhibited method is the proof of the complete dichotomy for quotients of H.I. Banach spaces. Namely we show that every separable Banach space \(Z\) not containing an isomorphic copy of \(\ell^1\) is a quotient of a separable H.I. space \(X\). Furthermore the isomorph of \(Z^*\) into \(X^*\), defined by the conjugate operator of the quotient map, is a complemented subspace of \(X^*\).

Readership

Graduate students and research mathematicians interested in analysis.

  • Chapters
  • Introduction
  • 1. General results about H.I. spaces
  • 2. Schreier families and repeated averages
  • 3. The space $X = T[G, (\mathcal {S}_{n_j}, 1/m_j)_j, D]$ and the auxiliary space $T_{ad}$
  • 4. The basic inequality
  • 5. Special convex combinations in $X$
  • 6. Rapidly increasing sequences
  • 7. Defining $D$ to obtain a H.I. space $X_G$
  • 8. The predual $(X_G)_*$ of $X_G$ is also H.I.
  • 9. The structure of the space of operators $\mathcal {L}(X_G)$
  • 10. Defining $G$ to obtain a nonseparable H.I. space $X^*_G$
  • 11. Complemented embedding of $l^p$, $1 \leq p < \infty $, in the duals of H.I. spaces
  • 12. Compact families in $\mathbb {N}$
  • 13. The space $X_G = T[G, (\mathcal {S}_\xi , 1/m_j)_j, D]$ for an $\mathcal {S}_\xi $ bounded set $G$
  • 14. Quotients of H.I. 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
Please select which format for which you are requesting permissions.