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  "body": "\n## Example\n\nLet $c_{00}$ be the space of real sequences with finitely many nonzero terms.\nFor finite sets $E, F \\subset \\N$, write $E \u003c F$ when $\\max E \u003c \\min F$.\nFor $x \\in c_{00}$ and a finite set $E$, let $E x$ be the sequence equal to $x$ on $E$ and to $0$ off $E$.\nCall finite sets $E_1, \\dots, E_n$ admissible when $n \\le \\min E_1$ and $E_1 \u003c E_2 \u003c \\cdots \u003c E_n$.\nThere is exactly one norm on $c_{00}$ that satisfies\n$$\\norm{x} = \\max \\Big( \\norm{x}_\\infty, \\ \\frac{1}{2} \\sup \\sum_{j=1}^n \\norm{E_j x} \\Big),$$\nwhere the supremum runs over all $n$ and all admissible $E_1, \\dots, E_n$.\nThe completion $T$ of $c_{00}$ for this norm is the Tsirelson space.\nIt is a [[Banach space|06GZ956657]].\n\nCheck of two values.\nFor a unit vector $e_k$, at most one set $E_j$ meets $k$, so the sum is at most $\\norm{e_k}$, and the equation gives $\\norm{e_k} = 1$.\nFor $x = e_{n+1} + \\cdots + e_{2n}$, the sets $\\set{n+1}, \\dots, \\set{2n}$ are admissible, so $n/2 \\le \\norm{x} \\le n$.\n\n## Remarks\n\nThe unit vectors form an unconditional basis of $T$, and $T$ is [[reflexive|NN8RWPC8WG]].\nThe space $T$ contains no subspace isomorphic to $c_0$ or to any [[sequence space|08P6T2WH6R]] $\\ell^p$ with $1 \\le p \u003c \\infty$.\nTsirelson built the first space with this property in 1974.\nThe space above, described by Figiel and Johnson, is the dual of Tsirelson's original space.\nThe second check shows how the norm forces blocks far out in the sequence to behave like $\\ell^1$ of their length.\n\n## Explanations\n\n### L1 human\n\nFor a long time it was open whether every Banach space contains a copy of one of the classical sequence spaces.\nTsirelson space shows that the answer is no.\nIts norm is defined by an equation that refers to itself.\nThis rule makes the space look like $\\ell^1$ on short blocks and stops it from containing any classical space as a whole.\n",
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