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I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553.
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127.
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49.

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553.
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127.
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49.

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553.
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127.
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49.

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

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Martin Sleziak
Martin Sleziak
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I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553.
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127.
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49.

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553.
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127.
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49.

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

added 1 character in body
Source Link
Martin Sleziak
Martin Sleziak
  • 4.7k
  • 4
  • 35
  • 40

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553
  • Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

I am posting a CW answer. Feel free to add other references.

Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yields a Banach space).

Books

  • Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite dimensional analysis: A hitchhiker's guide (Third ed.). Berlin: Springer; page 553
  • Megginson, Robert E. (1998). An Introduction to Banach Space Theory. Graduate Texts in Mathematics. 193. New York: Springer; Exercise 5.1.
  • A. Ya. Helemskii: Lectures and exercises on functional analysis, AMS 2006; Proposition 1.1.7 and remark on page 127
  • N. L. Carothers: A Short Course on Banach Space Theory, CUP, 2004; page 49

Online resources

Searches

This construction is sometimes called the $l_p$-sum of Banach spaces $X_1,X_2,\dots$. If we know the name, this might help it finding at least some references if we search for this name with some reasonable additional keywords:

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Martin Sleziak
Martin Sleziak
  • 4.7k
  • 4
  • 35
  • 40