diff --git a/src/tensors/linalg.jl b/src/tensors/linalg.jl
index 38c45c1f9..d174bef71 100644
--- a/src/tensors/linalg.jl
+++ b/src/tensors/linalg.jl
@@ -269,8 +269,9 @@ function _norm(blockiter, p::Real, init::Real)
             return isempty(b) ? init : oftype(init, LinearAlgebra.normInf(b))
         end
     elseif p > 0 # finite positive p
-        np = sum(blockiter; init) do (c, b)
-            return oftype(init, dim(c) * norm(b, p)^p)
+        np = init
+        for (c, b) in blockiter
+            np += oftype(init, dim(c) * norm(b, p)^p)
         end
         return np^(inv(oftype(np, p)))
     else
@@ -278,6 +279,12 @@ function _norm(blockiter, p::Real, init::Real)
         throw(ArgumentError(msg))
     end
 end
+function LinearAlgebra.norm(t::TensorMap, p::Real = 2)
+    InnerProductStyle(t) === EuclideanInnerProduct() || throw_invalid_innerproduct(:norm)
+    # performance specialization:
+    FusionStyle(sectortype(t)) isa UniqueFusion && return norm(t.data, p)
+    return _norm(blocks(t), p, float(zero(real(scalartype(t)))))
+end
 
 _default_rtol(t) = eps(real(float(scalartype(t)))) * min(dim(domain(t)), dim(codomain(t)))